R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 1 - Number Systems

Chapter 1 - Number Systems Exercise VSAQ

Question 1

What can you say about the sum of a rational number and an irrational number?

Solution 1

The sum of a rational number and an irrational number is irrational.

Example: 5 + R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is irrational. 

Question 2

Solve R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3

The number R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems will terminate after how many decimal places?

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Thus, the given number will terminate after 3 decimal places. 

Question 4

Find the value of (1296)0.17× (1296)0.08. 

Solution 4

(1296)0.17× (1296)0.08

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 5

Simplify R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 6

Find an irrational number between 5 and 6.

Solution 6

An irrational number between 5 and 6 = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 7

Find the value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8

Rationalise R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 9

Solve for x: R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 10

Simplify (32)1/5 + (-7)0 + (64)1/2.

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 11

Evaluate R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 12

Simplify R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 13

If a = 1, b = 2 then find the value of (ab + ba)-1.

Solution 13

Given, a = 1 and b = 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 14

Simplify R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 15

Give an example of two irrational numbers whose sum as well as product is rational.

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 16

Is the product of a rational and irrational numbers always irrational? Give an example.

Solution 16

Yes, the product of a rational and irrational numbers is always irrational.

For example,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 17

Give an example of a number x such that x2 is an irrational number and x3 is a rational number.

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 18

Write the reciprocal of (R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems).

Solution 18

The reciprocal of (R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 20

Simplify R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 21

If 10x = 64, find the value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 22

Evaluate R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 23

Simplify R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Chapter 1 - Number Systems Exercise MCQ

Question 1

Which of the following is a rational number?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) π

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) 0

Solution 1

Correct option: (d)

0 can be written as R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems where p and q are integers and q ≠ 0.

Question 2

A rational number between -3 and 3 is

(a) 0

(b) -4.3

(c) -3.4

(d) 1.101100110001....

Solution 2

Correct option: (a)

On a number line, 0 is a rational number that lies between -3 and 3. 

Question 3

Two rational numbers between R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems are

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Two rational numbers between R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems  

Question 4

Every point on number line represents

(a) a rational number

(b) a natural number

(c) an irrational number

(d) a unique number

Solution 4

Correct option: (d)

Every point on number line represents a unique number. 

Question 5

Which of the following is a rational number?

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 6

Every rational number is

(a) a natural number

(b) a whole number

(c) an integer

(d)a real number

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 7

Between any two rational numbers there

(a) is no rational number

(b) is exactly one rational number

(c) are infinitely many rational numbers

(d)is no irrational number

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 8

The decimal representation of a rational number is

(a) always terminating

(b) either terminating or repeating

(c) either terminating or non-repeating

(d)neither terminating nor repeating

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 9

The decimal representation of an irrational number is

(a) always terminating

(b) either terminating or repeating

(c) either terminating or non-repeating

(d)neither terminating nor repeating

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 10

The decimal expansion that a rational number cannot have is

(a) 0.25

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) 0.5030030003....

Solution 10

Correct option: (d)

The decimal expansion of a rational number is either terminating or non-terminating recurring.

The decimal expansion of 0.5030030003…. is non-terminating non-recurring, which is not a property of a rational number. 

Question 11

Which of the following is an irrational number?

(a) 3.14

(b) 3.141414....

(c) 3.14444.....

(d) 3.141141114....

Solution 11

Correct option: (d)

The decimal expansion of an irrational number is non-terminating non-recurring.

Hence, 3.141141114….. is an irrational number. 

Question 12

A rational number equivalent to R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 12

Correct option: (d)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 13

Choose the rational number which does not lie between R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 13

Correct option: (b)

Given two rational numbers are negative and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is a positive rational number.

So, it does not lie between R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 14

Π is

(a) a rational number

(b) an integer

(c) an irrational number

(d) a whole number

Solution 14

Correct option: (c)

Π = 3.14159265359…….., which is non-terminating non-recurring.

Hence, it is an irrational number.

Question 15

The decimal expansion of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) finite decimal

(b) 1.4121

(c) nonterminating recurring

(d) nonterminating, nonrecurring

Solution 15

Correct option: (d)

The decimal expansion of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, which is non-terminating, non-recurring. 

Question 16

Which of the following is an irrational number?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) 0.3799

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 16

Correct option: (a)

The decimal expansion of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, which is non-terminating, non-recurring.

Hence, it is an irrational number. 

Question 17

Hoe many digits are there in the repeating block of digits in the decimal expansion of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(a) 16

(b) 6

(c) 26

(d) 7

Solution 17

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 18

Which of the following numbers is irrational?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 18

Correct option: (c)

The decimal expansion of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, which is non-terminating, non-recurring.

Hence, it is an irrational number. 

Question 19

The product of two irrational numbers is

(a) always irrational

(b) always rational

(c) always an integer

(d)sometimes rational and sometimes irrational

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 20

Which of the following is a true statement?

(a) The sum of two irrational numbers is an irrational number

(b) The product of two irrational numbers is an irrational number

(c) Every real number is always rational

(d) Every real number is either rational or irrational

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 21

Which of the following is a true statement?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 22

A rational number lying between R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) 1.6

(d) 1.9

Solution 22

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 23

Which of the following is a rational number?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) 0.101001000100001...

(c) π 

(d) 0.853853853...

Solution 23

Correct option: (d)

The decimal expansion of a rational number is either terminating or non-terminating recurring.

Hence, 0.853853853... is a rational number. 

Question 24

The product of a nonzero rational number with an irrational number is always a/an

(a) irrational number

(b) rational number

(c) whole number

(d) natural number

Solution 24

Correct option: (a)

The product of a non-zero rational number with an irrational number is always an irrational number. 

Question 25

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p and q are integers and q 0, is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 25

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 30

An irrational number between 5 and 6 is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 31

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 31

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 33

The sum of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 33

Correct option: (b)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 0.3333…. ….(i)

10x = 3.3333…. ….(ii)

On subtracting (i) from (ii), we get

9x = 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Let y = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. y = 0.4444…. ….(i)

10y = 4.4444…. ….(ii)

On subtracting (i) from (ii), we get

9y = 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 34

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 34

Correct option: (c)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 2.4545….  ….(i)

100x = 245.4545…….  ….(ii)

On subtracting (i) from (ii), we get

99x = 243

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Let y = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

i.e. y = 0.3636….  ….(iii)

100y = 36.3636….  ….(iv)

On subtracting (iii) from (iv), we get

99y = 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 35

Which of the following is the value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems?

(a) -4

(b) 4

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 35

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems when simplified is

(a) positive and irrational

(b) positive and rational

(c) negative and irrational

(d) negative and rational

Solution 36

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Which is positive and rational number. 

Question 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems when simplified is

(a) positive and irrational

(b) positive and rational

(c) negative and irrational

(d) negative and rational

Solution 37

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Which is positive and rational number. 

Question 38

When R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is divided by R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, the quotient is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 38

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 39

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) 10

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 39

Correct option: (a)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 40

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 40

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 41

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems= ?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) None of these

Solution 41

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 42

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems=?

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) 2

(c) 4

(d) 8

Solution 42

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 43

(125)-1/3 = ?

(a) 5

(b) -5

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 43

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 44

The value of 71/2 81/2 is

(a) (28)1/2

(b) (56)1/2

(c) (14)1/2

(d) (42)1/2

Solution 44

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 45

After simplification, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) 132/15

(b) 138/15

(c) 131/3

(d) 13-2/15

Solution 45

Correct option: (d)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 46

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsis

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) 8

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 46

Correct option: (a)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 47

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsis

(a) 0

(b) 2

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 47

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 48

The value of (243)1/5 is

(a) 3

(b) -3

(c) 5

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 48

Correct option: (a)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 49

93 + (-3)3 - 63 = ?

(a) 432

(b) 270

(c) 486

(d) 540

Solution 49

Correct option: (c)

93 + (-3)3 - 63 = 729 - 27 - 216 = 486 

Question 50

Simplified value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) 0

(b) 1

(c) 4

(d) 16

Solution 50

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 51

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsis

(a) 2-1/6

(b) 2-6

(c) 21/6

(d) 26

Solution 51

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 52

Simplified value of (25)1/3× 51/3 is

(a) 25

(b) 3

(c) 1

(d) 5

Solution 52

Correct option: (d)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 53

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsis

(a) 3

(b) -3

(c) 9

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 53

Correct option: (a)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 54

There is a number x such that x2 is irrational but x4 is rational. Then, x can be

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 54

Correct option: (d)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 55

If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems then value of p is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 55

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 56

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsis

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 56

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 57

The value of xp-q xq - r xr - p is equal to

(a) 0

(b) 1

(c) x

(d) xpqr

Solution 57

Correct option: (b)

xp-q xq - r xr - p

= xp - q + q - r + r - p

= x0

= 1 

Question 58

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) -1

(b) 0

(c) 1

(d) 2

Solution 58

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 59

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems= ?

(a) 2

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 59

Correct option: (a)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 60

If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems then x = ?

(a) 1

(b) 2

(c) 3

(d) 4

Solution 60

Correct option: (d)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 61

If (33)2 = 9x then 5x = ?

(a) 1

(b) 5

(c) 25

(d) 125

Solution 61

Correct option: (d)

(33)2 = 9x

(32)3 = (32)x

x = 3

Then 5x = 53 = 125 

Question 62

On simplification, the expression R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems equals

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 62

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 63

The simplest rationalisation factor of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 63

Correct option: (d)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Thus, the simplest rationalisation factr of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems  

Question 64

The simplest rationalisation factor of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 

Solution 64

Correct option: (b)

The simplest rationalisation factor of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 65

The rationalisation factor of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 65

Correct option: (d)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 66

Rationalisation of the denominator of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems gives

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 66

Correct option: (d)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 67

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) 2

(c) 4

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 67

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 68

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) None of these

Solution 68

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 69

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) 14

(c) 49

(d) 48

Solution 69

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 70

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(a) 0.075

(b) 0.75

(c) 0.705

(d) 7.05

Solution 70

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 71

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(a) 0.375

(b) 0.378

(c) 0.441

(d) None of these

Solution 71

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 72

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 72

Correct option: (d)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 73

The value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is

(a) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(b) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(c) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(d) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 73

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 74

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(a) 0.207

(b) 2.414

(c) 0.414

(d) 0.621

Solution 74

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 75

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems= ?

(a) 34

(b) 56

(c) 28

(d) 63

Solution 75

Correct option: (a)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 76

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

 

Assertion (A)

Reason (R)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

A rational number between two rational numbers p and q is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

 

The correct answer is: (a)/(b)/(c)/(d).

Solution 76

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 77

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

 

Assertion (A)

Reason (R)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Square root of a positive integer which is not a perfect square is an irrational number.

 

The correct answer is: (a)/(b)/(c)/(d).

Solution 77

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 78

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

 

Assertion (A)

Reason (R)

e is an irrational number.

Π is an irrational number.

 

The correct answer is: (a)/(b)/(c)/(d).

Solution 78

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 79

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

 

Assertion (A)

Reason (R)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

The sum of a rational number and an irrational number is an irrational number.

 

The correct answer is: (a)/(b)/(c)/(d).

Solution 79

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 80

Match the following columns:

Column I

Column II

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(p) 14

(q) 6

(r) a rational number

(s) an irrational number

 

The correct answer is:

(a)-…….,

(b)-…….,

(c)-…….,

(d)-…….,

Solution 80

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 81

Match the following columns:

Column I

Column II

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 

The correct answer is:

(a)-…….,

(b)-…….,

(c)-…….,

(d)-…….,

Solution 81

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Chapter 1 - Number Systems Exercise Ex. 1B

Question 1(i)

Without actual division, find which of the following rationals are terminating decimals.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

If the prime factors of the denominator are 2 and/or 5 then the rational number is a terminating decimal.

Since, 80 has prime factors 2 and 5, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is a terminating decimal.

Question 1(ii)

Without actual division, find which of the following rationals are terminating decimals.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

If the prime factors of the denominators of the fraction are other than 2 and 5, then the rational number is not a terminating decimal.

Since, 24 has prime factors 2 and 3 and 3 is different from 2 and 5,

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsis not a terminating decimal.

Question 1(iii)

Without actual division, find which of the following rationals are terminating decimals.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

If the prime factors of the denominators of the fraction are other than 2 and 5, then the rational number is not a terminating decimal.

Since 12 has prime factors 2 and 3  and 3 is different from 2 and 5,

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsis not a terminating decimal.

Question 1(iv)

Without actual division, find which of the following rational numbers are terminating decimals.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Since the denominator of a given rational number is not of the form 2m × 2n, where m and n are whole numbers, it has non-terminating decimal. 

Question 2(i)

Write each of the following in decimal form and say what kind of decimal expansion each has.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Hence, it has terminating decimal expansion. 

Question 2(ii)

Write each of the following in decimal form and say what kind of decimal expansion each has.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Hence, it has terminating decimal expansion. 

Question 2(iii)

Write each of the following in decimal form and say what kind of decimal expansion each has.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Hence, it has non-terminating recurring decimal expansion. 

Question 2(iv)

Write each of the following in decimal form and say what kind of decimal expansion each has.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Hence, it has non-terminating recurring decimal expansion. 

Question 2(v)

Write each of the following in decimal form and say what kind of decimal expansion each has.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Hence, it has non-terminating recurring decimal expansion. 

Question 2(vi)

Write each of the following in decimal form and say what kind of decimal expansion each has.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(vi)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Hence, it has terminating decimal expansion. 

Question 2(vii)

Write each of the following in decimal form and say what kind of decimal expansion each has.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(vii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Hence, it has terminating decimal expansion. 

Question 2(viii)

Write each of the following in decimal form and say what kind of decimal expansion each has.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(viii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Hence, it has non-terminating recurring decimal expansion. 

Question 3(i)

Express each of the following decimals in the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p, q are integers and q 0.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(i)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 0.2222…. ….(i)

10x = 2.2222…. ….(ii)

On subtracting (i) from (ii), we get

9x = 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(ii)

Express each of the following decimals in the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p, q are integers and q 0.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(ii)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 0.5353….  ….(i)

100x = 53.535353…. ….(ii)

On subtracting (i) from (ii), we get

99x = 53

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(iii)

Express each of the following decimals in the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p, q are integers and q 0.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(iii)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 2.9393….  ….(i)

100x = 293.939……. ….(ii)

On subtracting (i) from (ii), we get

99x = 291

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(iv)

Express each of the following decimals in the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p, q are integers and q 0.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(iv)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 18.4848….  ….(i)

100x = 1848.4848……. ….(ii)

On subtracting (i) from (ii), we get

99x = 1830

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(v)

Express each of the following decimals in the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p, q are integers and q 0.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(v)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 0.235235..…   ….(i)

1000x = 235.235235……. ….(ii)

On subtracting (i) from (ii), we get

999x = 235

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(vi)

Express each of the following decimals in the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p, q are integers and q 0.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(vi)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 0.003232..…   

100x = 0.323232……. ….(i)

10000x = 32.3232…. ….(ii)

On subtracting (i) from (ii), we get

9900x = 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(vii)

Express each of the following decimals in the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p, q are integers and q 0.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(vii)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 1.3232323..… ….(i)   

100x = 132.323232……. ….(ii)

On subtracting (i) from (ii), we get

99x = 131

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(viii)

Express each of the following decimals in the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p, q are integers and q 0.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(viii)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 0.3178178..… 

10x = 3.178178…… ….(i)   

10000x = 3178.178……. ….(ii)

On subtracting (i) from (ii), we get

9990x = 3175

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(ix)

Express each of the following decimals in the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p, q are integers and q 0.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(ix)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 32.123535..… 

100x = 3212.3535…… ….(i)   

10000x = 321235.3535……. ….(ii)

On subtracting (i) from (ii), we get

9900x = 318023

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(x)

Express each of the following decimals in the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where p, q are integers and q 0.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(x)

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 0.40777..… 

100x = 40.777…… ….(i)   

1000x = 407.777……. ….(ii)

On subtracting (i) from (ii), we get

900x = 367

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 4

Express R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsas a fraction in simplest form.

Solution 4

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. x = 2.3636….  ….(i)

100x = 236.3636……. ….(ii)

On subtracting (i) from (ii), we get

99x = 234

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Let y = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

i.e. y = 0.2323….  ….(iii)

100y = 23.2323…. ….(iv)

On subtracting (iii) from (iv), we get

99y = 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 5

Express in the form of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Solution 5

Let x = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

i.e. x = 0.3838….  ….(i)

100x = 38.3838….  ….(ii)

On subtracting (i) from (ii), we get

99x = 38

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Let y = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

i.e. y = 1.2727….  ….(iii)

100y = 127.2727…….  ….(iv)

On subtracting (iii) from (iv), we get

99y = 126

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 9(v)

Without actual division, find which of the following rationals are terminating decimals.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 9(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

If the prime factors of the denominator are 2 and/or 5 then the rational number is a terminating decimal.

 

Since 125 has prime factor 5 only

  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is a terminating decimal.

Chapter 1 - Number Systems Exercise Ex. 1C

Question 1

What are irrational numbers? How do they differ from rational numbers? Give examples.

Solution 1

Irrational number: A number which cannot be expressed either as a terminating decimal or a repeating decimal is known as irrational number. Rather irrational numbers cannot be expressed in the fraction form, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

For example, 0.101001000100001 is neither a terminating nor a repeating decimal and so is an irrational number.

Also, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsetc. are examples of irrational numbers.

Question 2(iii)

Classify the following numbers as rational or irrational. Give reasons to support you answer.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems


We know that, if n is a not a perfect square, then R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is an irrational number.

Here, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is a not a perfect square number.

So, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsis irrational.

Question 2(v)

Classify the following numbers as rational or irrational. Give reasons to support you answer.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is the product of a rational number R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems and an irrational number R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Theorem: The product of a non-zero rational number and an irrational number is an irrational number.

Thus, by the above theorem, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is an irrational number.

So, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is an irrational number.

Question 2(i)

Classify the following numbers as rational or irrational. Give reasons to support your answer.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Since quotient of a rational and an irrational is irrational, the given number is irrational.  

Question 2(ii)

Classify the following numbers as rational or irrational. Give reasons to support your answer.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 2(iv)

Classify the following numbers as rational or irrational. Give reasons to support your answer.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 2(vi)

Classify the following numbers as rational or irrational. Give reasons to support your answer.

4.1276

Solution 2(vi)

The given number 4.1276 has terminating decimal expansion.

Hence, it is a rational number. 

Question 2(vii)

Classify the following numbers as rational or irrational. Give reasons to support your answer.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(vii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Since the given number has non-terminating recurring decimal expansion, it is a rational number. 

Question 2(viii)

Classify the following numbers as rational or irrational. Give reasons to support your answer.

1.232332333....

Solution 2(viii)

The given number 1.232332333.... has non-terminating and non-recurring decimal expansion.

Hence, it is an irrational number. 

Question 2(ix)

Classify the following numbers as rational or irrational. Give reasons to support your answer.

3.040040004.....

Solution 2(ix)

The given number 3.040040004..... has non-terminating and non-recurring decimal expansion.

Hence, it is an irrational number. 

Question 2(x)

Classify the following numbers as rational or irrational. Give reasons to support your answer.

2.356565656.....

Solution 2(x)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

The given number 2.356565656..... has non-terminating recurring decimal expansion.

Hence, it is a rational number. 

Question 2(xi)

Classify the following numbers as rational or irrational. Give reasons to support your answer.

6.834834....

Solution 2(xi)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

The given number 6.834834.... has non-terminating recurring decimal expansion.

Hence, it is a rational number. 

Question 3

Let x be a rational number and y be an irrational number. Is x + y necessarily an irrational number? Give an example in support of your answer.

Solution 3

We know that the sum of a rational and an irrational is irrational.

Hence, if x is rational and y is irrational, then x + y is necessarily an irrational number.

For example,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 4

Let a be a rational number and b be an irrational number. Is ab necessarily an irrational number? Justify your answer with an example.

Solution 4

We know that the product of a rational and an irrational is irrational.

Hence, if a is rational and b is irrational, then ab is necessarily an irrational number.

For example,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 5

Is the product of two irrationals always irrational? Justify your answer.

Solution 5

No, the product of two irrationals need not be an irrational.

For example,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 6

Give an example of two irrational numbers whose

(i) difference is an irrational number.

(ii) difference is a rational number.

(iii) sum is an irrational number.

(iv) sum is an rational number.

(v) product is an irrational number.

(vi) product is a rational number.

(vii) quotient is an irrational number.

(viii) quotient is a rational number. 

Solution 6

(i) Difference is an irrational number:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(ii) Difference is a rational number:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(iii) Sum is an irrational number:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(iv) Sum is an rational number:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(v) Product is an irrational number:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(vi) Product is a rational number:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(vii) Quotient is an irrational number:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

(viii) Quotient is a rational number:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 7

Examine whether the following numbers are rational or irrational.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8

Insert a rational and an irrational number between 2 and 2.5

Solution 8

Rational number between 2 and 2.5 = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Irrational number between 2 and 2.5 = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 9

How many irrational numbers lie betweenR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems? Find any three irrational numbers lying between R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 9

There are infinite irrational numbers betweenR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

We have

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Hence, three irrational numbers lying between R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems are as follows:

1.5010010001……., 1.6010010001…… and 1.7010010001……. 

Question 10

Find two rational and two irrational numbers between 0.5 and 0.55.

Solution 10

Since 0.5 < 0.55

Let x = 0.5, y = 0.55 and y = 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Two irrational numbers between 0.5 and 0.55 are 0.5151151115……. and 0.5353553555…. 

Question 11

Find three different irrational numbers between the rational numbers R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Thus, three different irrational numbers between the rational numbers R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems are as follows:

0.727227222….., 0.757557555….. and 0.808008000….. 

Question 12

Find two rational numbers of the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsbetween the numbers 0.2121121112... and  0.2020020002......

Solution 12

Let a and b be two rational numbers between the numbers 0.2121121112... and 0.2020020002......

Now, 0.2020020002...... <0.2121121112...

Then, 0.2020020002...... < a < b < 0.2121121112...

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 13

Find two irrational numbers between 0.16 and 0.17.

Solution 13

Two irrational numbers between 0.16 and 0.17 are as follows:

0.1611161111611111611111…… and 0.169669666……. 

Question 14(i)

State in each case, whether the given statement is true or false.

The sum of two rational numbers is rational.

Solution 14(i)

True

Question 14(ii)

State in each case, whether the given statement is true or false.

The sum of two irrational numbers is irrational.

Solution 14(ii)

False

Question 14(iii)

State in each case, whether the given statement is true or false.

The product of two rational numbers is rational.

Solution 14(iii)

True

Question 14(iv)

State in each case, whether the given statement is true or false.

The product of two irrational numbers is irrational.

Solution 14(iv)

False

Question 14(v)

State in each case, whether the given statement is true or false.

The sum of a rational number and an irrational number is irrational.

Solution 14(v)

True

Question 14(vi)

State in each case, whether the given statement is true or false.

The product of a nonzero rational number and an irrational number is a rational number.

Solution 14(vi)

False

Question 14(vii)

State in each case, whether the given statement is true or false.

Every real number is rational.

Solution 14(vii)

False

Question 14(viii)

State in each case, whether the given statement is true or false.

Every real number is either rational or irrational.

Solution 14(viii)

True

Question 14(ix)

State in each case, whether the given statement is true or false.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsis irrational and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsis rational.

Solution 14(ix)

True

Chapter 1 - Number Systems Exercise Ex. 1D

Question 1(i)

Add:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

We have:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 1(ii)

Add:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

We have:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 1(iii)

Add:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(i)

Multiply:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 

 

 

Question 2(ii)

Multiply:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(iii)

Multiply:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(iv)

Multiply:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 

 

 

Question 2(v)

Multiply:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 

 

 

Question 2(vi)

Multiply:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(vi)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 

 

Question 3(i)

Divide:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 3(ii)

Divide:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 3(iii)

Divide:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 4(iii)

Simplify:

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 4(iv)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 4(vi)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(vi)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 4(i)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

= 9 - 11

= -2  

Question 4(ii)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

= 9 - 5

= 4 

Question 4(v)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 5

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 6(i)

Examine whether the following numbers are rational or irrational:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 6(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Thus, the given number is rational. 

Question 6(ii)

Examine whether the following numbers are rational or irrational:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 6(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Clearly, the given number is irrational. 

Question 6(iii)

Examine whether the following numbers are rational or irrational:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 6(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Thus, the given number is rational. 

Question 6(iv)

Examine whether the following numbers are rational or irrational:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 6(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Thus, the given number is irrational. 

Question 7

On her birthday Reema distributed chocolates in an orphanage. The total number of chocolates she distributed is given by R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

(i) Find the number of chocolates distributed by her.

(ii) Write the moral values depicted here by Reema.

Solution 7

(i) Number of chocolates distributed by Reema

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

 

(ii) Loving, helping and caring attitude towards poor and needy children.

Question 8(i)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 8(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8(ii)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 8(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8(iii)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 8(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Chapter 1 - Number Systems Exercise Ex. 1G

Question 1(iii)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 1(i)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 1(ii)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 1(iv)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 1(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 2(i)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(ii)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(iii)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 3(i)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 3(ii)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 3(iii)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 4(i)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 4(ii)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 4(iii)

Simplify:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 5(i)

Evaluate:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 5(ii)

Evaluate:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 

Question 5(iii)

Evaluate:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 5(iv)

Evaluate:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 5(v)

Evaluate:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 5(vi)

Evaluate:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(vi)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 6(i)

If a = 2, b = 3, find the value of (ab + ba)-1

Solution 6(i)

Given, a = 2 and b = 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 6(ii)

If a = 2, b = 3, find the value of (aa + bb)-1

Solution 6(ii)

Given, a = 2 and b = 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 7(i)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 7(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 7(ii)

Simplify

(14641)0.25

Solution 7(ii)

(14641)0.25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 7(iii)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 7(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 7(iv)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 7(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8(i)

Evaluate

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 8(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8(ii)

Evaluate

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 8(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8(iii)

Evaluate

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 8(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8(iv)

Evaluate

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 8(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 9(i)

Evaluate

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 9(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 9(ii)

Evaluate

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 9(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 9(iii)

Evaluate

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 9(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 9(iv)

Evaluate

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 9(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 10(i)

Prove that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 10(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 10(ii)

Prove that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 10(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 10(iii)

Prove that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 10(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 11

Simplify R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsand express the result in the exponential form of x.

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 12

Simplify the product R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 13(i)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 13(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 13(ii)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 13(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 13(iii)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 13(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 14(i)

Find the value of x in each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 14(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 14(ii)

Find the value of x in each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 14(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 14(iii)

Find the value of x in each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 14(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 14(iv)

Find the value of x in each of the following.

5x - 3× 32x - 8 = 225

Solution 14(iv)

5x - 3 × 32x - 8 = 225

5x - 3× 32x - 8 = 52 × 32

x - 3 = 2 and 2x - 8 = 2

x = 5 and 2x = 10

x = 5 

Question 14(v)

Find the value of x in each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 14(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 15(i)

Prove that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 15(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 15(ii)

Prove that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 15(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 15(iii)

Prove that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 15(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 15(iv)

Prove that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 15(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 16

If x is a positive real number and exponents are rational numbers, simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 17

If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsprove that m - n = 1.

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 18

Write the following in ascending order of magnitude.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Chapter 1 - Number Systems Exercise Ex. 1A

Question 1

Is zero a rational number? Justify.

Solution 1

A number which can be expressed as R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, where 'a' and 'b' both are integers and b ≠ 0, is called a rational number.

Since, 0 can be expressed as R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, it is a rational number.

Question 2(i)

Represent each of the following rational numbers on the number line:

(i) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(i)

(i)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 

Question 2(ii)

Represent each of the following rational numbers on the number line:

(ii) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(ii)

(ii)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(iii)

Represent each of the following rational numbers on the number line:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 2(iv)

Represent each of the following rational numbers on the number line:

(iv) 1.3

Solution 2(iv)

(iv) 1.3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(v)

Represent each of the following rational numbers on the number line:

(v) -2.4

Solution 2(v)

(v) -2.4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 3(i)

Find a rational number lying between

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 3(ii)

Find a rational number lying between

1.3 and 1.4

Solution 3(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 3(iii)

Find a rational number lying between

-1 and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 3(iv)

Find a rational number lying between

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 3(v)

Find a rational number between

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 4

Find three rational numbers lying between R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

How many rational numbers can be determined between these two numbers?

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Infinite rational numbers can be determined between given two rational numbers.

Question 5

Find four rational numbers between R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5

We have

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

We know that 9 < 10 < 11 < 12 < 13 < 14 < 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 6

Find six rational numbers between 2 and 3.

Solution 6

2 and 3 can be represented asR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsrespectively.

Now six rational numbers between 2 and 3 are 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems. 

Question 7

Find five rational numbers between R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8

Insert 16 rational numbers between 2.1 and 2.2.

Solution 8

Let x = 2.1 and y = 2.2

Then, x < y because 2.1 < 2.2

Or we can say that, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Or, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

That is, we have, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

We know that,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Therefore, we can have,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Therefore, 16 rational numbers between, 2.1 and 2.2 are:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

So, 16 rational numbers between 2.1 and 2.2 are:

2.105, 2.11, 2.115, 2.12, 2.125, 2.13, 2.135, 2.14, 2.145, 2.15, 2.155, 2.16, 2.165, 2.17, 2.175, 2.18



Question 9(i)

State whether the given statement is true or false. Give reasons. for your answer.

Every natural number is a whole number.

Solution 9(i)

True. Since the collection of natural number is a sub collection of whole numbers, and every element of natural numbers is an element of whole numbers

Question 9(ii)

Write, whether the given statement is true or false. Give reasons.

Every whole number is a natural number.

Solution 9(ii)

False. Since 0 is whole number but it is not a natural number.

Question 9(iii)

State whether the following statements are true or false. Give reasons for your answer.

Every integer is a whole number.

Solution 9(iii)

False, integers include negative of natural numbers as well, which are clearly not whole numbers. For example -1 is an integer but not a whole number.

Question 9(iv)

Write, whether the given statement is true or false. Give reasons.

Ever integer is a rational number.

Solution 9(iv)

True. Every integer can be represented in a fraction form with denominator 1.

Question 9(v)

State whether the following statements are true or false. Give reasons for your answer.

 

Every rational number is an integer.

Solution 9(v)

False, integers are counting numbers on both sides of the number line i.e. they are both positive and negative while rational numbers are of the form R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems. Hence, Every rational number is not an integer but every integer is a rational number.

Question 9(vi)

Write, whether the given statement is true or false. Give reasons.

Every rational number is a whole number.

Solution 9(vi)

False. Since division of whole numbers is not closed under division, the value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, may not be a whole number.

Chapter 1 - Number Systems Exercise Ex. 1E

Question 1

Represent R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemson the number line.

Solution 1

Draw a number line as shown.

On the number line, take point O corresponding to zero.

Now take point A on number line such that OA = 2 units.

Draw perpendicular AZ at A on the number line and cut-off arc AB = 1 unit.

By Pythagoras Theorem,

OB2 = OA2 + AB2 = 22 + 12 = 4 + 1 = 5

OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Taking O as centre and OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems as radius draw an arc cutting real line at C.

Clearly, OC = OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Hence, C represents R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems on the number line.

Question 2

Locate R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemson the number line. 

Solution 2

Draw a number line as shown.

On the number line, take point O corresponding to zero.

Now take point A on number line such that OA = 1 unit.

Draw perpendicular AZ at A on the number line and cut-off arc AB = 1 unit.

By Pythagoras Theorem,

OB2 = OA2 + AB2 = 12 + 12 = 1 + 1 = 2

OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Taking O as centre and OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems as radius draw an arc cutting real line at C.

Clearly, OC = OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Thus, C represents R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems on the number line.

Now, draw perpendicular CY at C on the number line and cut-off arc CE = 1 unit.

By Pythagoras Theorem,

OE2 = OC2 + CE2 = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems2 + 12 = 2 + 1 = 3

OE = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Taking O as centre and OE = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems as radius draw an arc cutting real line at D.

Clearly, OD = OE = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Hence, D represents R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems on the number line. 

Question 3

Locate R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemson the number line.

Solution 3

Draw a number line as shown.

On the number line, take point O corresponding to zero.

Now take point A on number line such that OA = 3 units.

Draw perpendicular AZ at A on the number line and cut-off arc AB = 1 unit.

By Pythagoras Theorem,

OB2 = OA2 + AB2 = 32 + 12 = 9 + 1 = 10

OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Taking O as centre and OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems as radius draw an arc cutting real line at C.

Clearly, OC = OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Hence, C represents R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems on the number line. 

Question 4

Locate R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemson the number line. 

Solution 4

Draw a number line as shown.

On the number line, take point O corresponding to zero.

Now take point A on number line such that OA = 2 units.

Draw perpendicular AZ at A on the number line and cut-off arc AB = 2 units.

By Pythagoras Theorem,

OB2 = OA2 + AB2 = 22 + 22 = 4 + 4 = 8

OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Taking O as centre and OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems as radius draw an arc cutting real line at C.

Clearly, OC = OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Hence, C represents R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems on the number line. 

Question 5

Represent R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems geometrically on the number line.

Solution 5

Draw a line segment AB = 4.7 units and extend it to C such that BC = 1 unit.

Find the midpoint O of AC.

With O as centre and OA as radius, draw a semicircle.

Now, draw BD AC, intersecting the semicircle at D.

Then, BD = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems units.

With B as centre and BD as radius, draw an arc, meeting AC produced at E.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number SystemsThen, BE = BD = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems units. 

Question 6

Represent R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemson the number line.

Solution 6

Draw a line segment OB = 10.5 units and extend it to C such that BC = 1 unit.

Find the midpoint D of OC.

With D as centre and DO as radius, draw a semicircle.

Now, draw BE AC, intersecting the semicircle at E.

Then, BE = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems units.

With B as centre and BE as radius, draw an arc, meeting AC produced at F.

 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Then, BF = BE = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems units.

Question 7

Represent R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsgeometrically on the number line.

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Draw a line segment AB = 7.28 units and extend it to C such that BC = 1 unit.

Find the midpoint O of AC.

With O as centre and OA as radius, draw a semicircle.

Now, draw BD R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number SystemsAC, intersecting the semicircle at D.

Then, BD = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsunits.

With D as centre and BD as radius, draw an arc, meeting AC produced at E.

Then, BE = BD = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsunits.

Question 8

Represent R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems on the number line.

Solution 8

Draw a line segment OB = 9.5 units and extend it to C such that BC = 1 unit.

Find the midpoint D of OC.

With D as centre and DO as radius, draw a semicircle.

Now, draw BE AC, intersecting the semicircle at E.

Then, BE = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems units.

With B as centre and BE as radius, draw an arc, meeting AC produced at F.

Then, BF = BE = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems units.

Extend BF to G such that FG = 1 unit.

Then, BG = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

 

Question 9

Visualize the representation of 3.765 on the number line using successive magnification.

Solution 9

 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 10

Visualize the representation of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems on the number line up to 4 decimal places.

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Chapter 1 - Number Systems Exercise Ex. 1F

Question 1

Write the rationalising factor of the denominator in R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems. 

Solution 1

The rationalising factor of the denominator in R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 2(i)

Rationalise the denominator of following:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(i)

On multiplying the numerator and denominator of the given number by R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, we get

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems


Question 2(ii)

Rationalise the denominator of following:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(ii)

On multiplying the numerator and denominator of the given number by R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems, we get

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(iii)

Rationalise the denominator of following:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(iv)

Rationalise the denominator of following:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(v)

Rationalise the denominator of following:

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 2(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Question 2(vi)

Rationalise the denominator of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Solution 2(vi)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 2(vii)

Rationalise the denominator of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Solution 2(vii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 2(viii)

Rationalise the denominator of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Solution 2(viii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 2(ix)

Rationalise the denominator of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Solution 2(ix)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

find the value to three places of decimals, of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

find the value to three places of decimals, of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 3(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

find the value to three places of decimals, of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 3(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 4(i)

Find rational numbers a and b such that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 4(ii)

Find rational numbers a and b such that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 4(iii)

Find rational numbers a and b such that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 4(iv)

Find rational numbers a and b such that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 4(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 5(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

find to three places of decimals, the value of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 5(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

find to three places of decimals, the value of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 5(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

find to three places of decimals, the value of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 5(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

find to three places of decimals, the value of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 5(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

find to three places of decimals, the value of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(v)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 5(vi)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

find to three places of decimals, the value of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 5(vi)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 6(i)

Simplify by rationalising the denominator.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 6(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 6(ii)

Simplify by rationalising the denominator.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 6(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 7(i)

Simplify: R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 7(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

 

Question 7(ii)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 7(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 7(iii)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 7(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 7(iv)

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 7(iv)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8(i)

Prove that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 8(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 8(ii)

Prove that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 8(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 9

Find the values of a and b if

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems*Back answer incorrect 

Question 10

Simplify

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Thus, the given number is rational. 

Question 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

*Question modified 

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems.

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 22(i)

Rationalise the denominator of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 22(i)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 22(ii)

Rationalise the denominator of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 22(ii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 22(iii)

Rationalise the denominator of each of the following.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 22(iii)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems 

Question 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems

Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems