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

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)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

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 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 4

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 4

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

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

(iv) 1.3

Solution 5

(iv) 1.3

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

Question 6

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

(v) -2.4

Solution 6

(v) -2.4

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

Question 7

Find a rational number lying 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

Find a rational number lying between

1.3 and 1.4

Solution 8

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

Question 9

Find a rational number lying between

-1 and 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

Find a rational number lying between

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

Find a rational number between

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

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 12

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 13

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

Solution 13

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 14

Find six rational numbers between 2 and 3.

Solution 14

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 15

Find five rational numbers between 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

Insert 16 rational numbers between 2.1 and 2.2.

Solution 16

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 17

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

Every natural number is a whole number.

Solution 17

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 18

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

Every whole number is a natural number.

Solution 18

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

Question 19

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

Every integer is a whole number.

Solution 19

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 20

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

Ever integer is a rational number.

Solution 20

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

Question 21

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

 

Every rational number is an integer.

Solution 21

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 22

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

Every rational number is a whole number.

Solution 22

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. 1B

Question 1

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

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 2

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 2

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 3

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 3

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 4

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 4

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 5

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 5

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 6

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 6

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 7

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 7

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 8

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 8

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 9

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 9

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 10

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 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 

Hence, it has terminating decimal expansion. 

Question 11

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 11

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 12

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 12

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 13

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 13

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 14

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 14

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 15

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 15

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 16

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 16

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 17

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 17

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 18

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 18

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 19

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 19

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 20

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 20

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 21

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 21

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 22

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 22

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 23

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

Solution 23

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 24

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

Solution 24

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 25

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 25

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

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

Solution 2

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 3

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

Solution 3

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 4

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 4

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 5

Find two irrational numbers between 0.16 and 0.17.

Solution 5

Two irrational numbers between 0.16 and 0.17 are as follows:

0.1611161111611111611111…… and 0.169669666……. 

Question 6

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

The sum of two rational numbers is rational.

Solution 6

True

Question 7

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

The sum of two irrational numbers is irrational.

Solution 7

False

Question 8

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

The product of two rational numbers is rational.

Solution 8

True

Question 9

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

The product of two irrational numbers is irrational.

Solution 9

False

Question 10

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 10

True

Question 11

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 11

True

Question 12

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 12

False

Question 13

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

Every real number is rational.

Solution 13

False

Question 14

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

Every real number is either rational or irrational.

Solution 14

True

Question 15

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 15

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 16

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 16

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

Question 17

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 17

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 18

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 18

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

Question 19

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

3.040040004.....

Solution 19

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

Hence, it is an irrational number. 

Question 20

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 20

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 21

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

4.1276

Solution 21

The given number 4.1276 has terminating decimal expansion.

Hence, it is a rational number. 

Question 22

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 22

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 23

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

1.232332333....

Solution 23

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

Hence, it is an irrational number. 

Question 24

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

2.356565656.....

Solution 24

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 25

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

6.834834....

Solution 25

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 26

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 26

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 27

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 27

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 28

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

Solution 28

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 29

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 29

(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 30

Examine whether the following numbers are rational or irrational.

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

Insert a rational and an irrational number between 2 and 2.5

Solution 31

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 32

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 32

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……. 

Chapter 1 - Number Systems Exercise Ex. 1D

Question 1

Add:

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

Solution 1

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 2

Add:

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

We have:

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

Question 3

Add:

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

Solution 3

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

Question 4

Multiply:

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

Solution 4

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

 

 

 

Question 5

Multiply:

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

Multiply:

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

Solution 6

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

Question 7

Multiply:

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

Multiply:

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

Multiply:

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

Divide:

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

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

Question 11

Divide:

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

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

Question 12

Divide:

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

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

Question 13

Simplify

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 

= 9 - 11

= -2  

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 

= 9 - 5

= 4 

Question 15

Simplify:

 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

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

Question 16

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

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

Question 17

Simplify

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

Simplify:

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

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

Question 19

Simplify

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

Examine whether the following numbers are rational or irrational:

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 

Thus, the given number is rational. 

Question 21

Examine whether the following numbers are rational or irrational:

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 

Clearly, the given number is irrational. 

Question 22

Examine whether the following numbers are rational or irrational:

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 

Thus, the given number is rational. 

Question 23

Examine whether the following numbers are rational or irrational:

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 

Thus, the given number is irrational. 

Question 24

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 24

(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 25

Simplify

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 

Question 26

Simplify

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

Simplify

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 

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

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 2

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

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 = 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 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 = 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 5

Locate R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemson the number line. 

Solution 5

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 6

Represent R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems geometrically on the number line.

Solution 6

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 7

Represent R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemson the number line.

Solution 7

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 8

Represent R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systemsgeometrically on the number line.

Solution 8

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 9

Represent R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems on the number line.

Solution 9

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 10

Visualize the representation of 3.765 on the number line using successive magnification.

Solution 10

 

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

Simplify

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

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

Solution 3

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

Thus, the given number is rational. 

Question 4

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

Solution 4

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

Question 5

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

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

Solution 6

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

Question 7

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

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

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

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

*Question modified 

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 

Question 12

Rationalise the denominator of following:

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

Solution 12

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 13

Rationalise the denominator of following:

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

Solution 13

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 14

Rationalise the denominator of following:

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

Rationalise the denominator of following:

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

Rationalise the denominator of each of the following.

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

Rationalise the denominator of following:

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

Rationalise the denominator of each of the following.

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 

Question 19

Rationalise the denominator of each of the following.

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

Rationalise the denominator of each of the following.

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

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

Rationalise the denominator of each of the following.

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

Rationalise the denominator of each of the following.

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

Rationalise the denominator of each of the following.

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 

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 

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 29

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

Question 30

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 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 

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 31

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

Question 32

Find rational numbers a and b such that

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

Find rational numbers a and b such that

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

Solution 33

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

Question 34

Find rational numbers a and b such that

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

Solution 34

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

Question 35

Find rational numbers a and b such that

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

Solution 35

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 

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 36

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

Question 37

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 37

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

Question 38

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 38

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

Question 39

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 39

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

Question 40

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 40

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 

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 41

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

Question 42

Simplify by rationalising the denominator.

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

Solution 42

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

Question 43

Simplify by rationalising the denominator.

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

Solution 43

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

Question 44

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

Solution 44

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 45

Simplify

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

Solution 45

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

Question 46

Simplify

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

Solution 46

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

Question 47

Simplify

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

Solution 47

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

Question 48

Prove that

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

Solution 48

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

Question 49

Prove that

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

Solution 49

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

Question 50

Find the values of a and b if

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

Solution 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Number Systems*Back answer incorrect 

Chapter 1 - Number Systems Exercise Ex. 1G

Question 1

Simplify

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

Solution 1

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

Question 2

Simplify

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

Simplify:

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

Solution 3

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

Question 4

Simplify

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

Solution 4

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

Question 5

Prove that

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

Prove that

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

Solution 6

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

Question 7

Prove that

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

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 8

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

Question 9

Simplify the product 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

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

Simplify

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

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 13

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

Question 14

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

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

Question 15

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 15

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

Question 16

Find the value of x in each of the following.

5x - 3× 32x - 8 = 225

Solution 16

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 17

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 17

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

Question 18

Prove that

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 

Question 19

Prove that

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

Prove that

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

Prove that

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

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 22

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

Question 23

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

Solution 23

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

Question 24

Write the following in ascending order of magnitude.

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

Simplify:

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

Question 26

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Solution 33

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

Question 34

Evaluate:

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

Solution 34

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

Question 35

Evaluate:

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

Solution 35

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

 

Question 36

Evaluate:

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

Solution 36

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

Question 37

Evaluate:

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

Solution 37

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

Question 38

Evaluate:

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

Solution 38

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

Question 39

Evaluate:

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

Solution 39

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

Question 40

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

Solution 40

Given, a = 2 and b = 3

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

Question 41

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

Solution 41

Given, a = 2 and b = 3

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

Question 42

Simplify

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

Solution 42

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

Question 43

Simplify

(14641)0.25

Solution 43

(14641)0.25

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

Question 44

Simplify

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

Solution 44

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

Question 45

Simplify

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

Solution 45

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

Question 46

Evaluate

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

Solution 46

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

Question 47

Evaluate

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

Solution 47

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

Question 48

Evaluate

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

Solution 48

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

Question 49

Evaluate

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

Solution 49

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

Question 50

Evaluate

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

Solution 50

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

Question 51

Evaluate

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

Solution 51

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

Question 52

Evaluate

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

Solution 52

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

Question 53

Evaluate

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

Solution 53

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

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 2

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 3

Which of the following is an irrational number?

(a) 3.14

(b) 3.141414....

(c) 3.14444.....

(d) 3.141141114....

Solution 3

Correct option: (d)

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

Hence, 3.141141114….. is an irrational number. 

Question 4

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 4

Correct option: (d)

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

Question 5

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 5

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 6

Π is

(a) a rational number

(b) an integer

(c) an irrational number

(d) a whole number

Solution 6

Correct option: (c)

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

Hence, it is an irrational number.

Question 7

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 7

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 8

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 8

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 9

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 9

Correct option: (b)

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

Question 10

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 10

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 11

The product of two irrational numbers is

(a) always irrational

(b) always rational

(c) always an integer

(d)sometimes rational and sometimes irrational

Solution 11

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

Question 12

A rational number between -3 and 3 is

(a) 0

(b) -4.3

(c) -3.4

(d) 1.101100110001....

Solution 12

Correct option: (a)

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

Question 13

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 13

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

Question 14

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 14

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

Question 15

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 15

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 16

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 16

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 17

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 17

Correct option: (a)

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

Question 18

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 18

Correct option: (b)

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

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

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 23

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 24

An irrational number between 5 and 6 is

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

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

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 27

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 28

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 28

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 29

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 29

Correct option: (b)

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

Question 30

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 30

Correct option: (b)

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

Which is positive and rational number. 

Question 31

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 31

Correct option: (b)

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

Which is positive and rational number. 

Question 32

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 32

Correct option: (c)

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

Question 33

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 33

Correct option: (a)

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

Question 34

Every point on number line represents

(a) a rational number

(b) a natural number

(c) an irrational number

(d) a unique number

Solution 34

Correct option: (d)

Every point on number line represents a unique number. 

Question 35

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 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= ?

(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 36

Correct option: (b)

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

Question 37

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 37

Correct option: (b)

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

Question 38

(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 38

Correct option: (c)

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

Question 39

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 39

Correct option: (b)

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

Question 40

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 40

Correct option: (d)

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

Question 41

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 41

Correct option: (a)

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

Question 42

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 42

Correct option: (b)

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

Question 43

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 43

Correct option: (a)

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

Question 44

93 + (-3)3 - 63 = ?

(a) 432

(b) 270

(c) 486

(d) 540

Solution 44

Correct option: (c)

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

Question 45

Which of the following is a rational number?

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

Solution 45

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

Question 46

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 46

Correct option: (b)

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) 2-1/6

(b) 2-6

(c) 21/6

(d) 26

Solution 47

Correct option: (c)

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

Question 48

Simplified value of (25)1/3× 51/3 is

(a) 25

(b) 3

(c) 1

(d) 5

Solution 48

Correct option: (d)

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

Question 49

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 49

Correct option: (a)

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

Question 50

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 50

Correct option: (d)

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

Question 51

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 51

Correct option: (b)

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

Question 52

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 52

Correct option: (b)

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

Question 53

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

(a) 0

(b) 1

(c) x

(d) xpqr

Solution 53

Correct option: (b)

xp-q xq - r xr - p

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

= x0

= 1 

Question 54

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 54

Correct option: (c)

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

Question 55

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 55

Correct option: (a)

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

Question 56

Every rational number is

(a) a natural number

(b) a whole number

(c) an integer

(d)a real number

Solution 56

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

Question 57

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 57

Correct option: (d)

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

Question 58

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

(a) 1

(b) 5

(c) 25

(d) 125

Solution 58

Correct option: (d)

(33)2 = 9x

(32)3 = (32)x

x = 3

Then 5x = 53 = 125 

Question 59

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 59

Correct option: (b)

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

Question 60

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 60

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 61

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 61

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 62

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 62

Correct option: (d)

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

Question 63

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 63

Correct option: (d)

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

Question 64

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 64

Correct option: (c)

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

Question 65

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 65

Correct option: (c)

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

Question 66

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 66

Correct option: (b)

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

Question 67

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 67

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) 0.075

(b) 0.75

(c) 0.705

(d) 7.05

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) 0.375

(b) 0.378

(c) 0.441

(d) None of these

Solution 69

Correct option: (b)

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

Question 70

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 70

Correct option: (d)

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

Question 71

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 71

Correct option: (c)

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

Question 72

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 72

Correct option: (c)

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

Question 73

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

(a) 34

(b) 56

(c) 28

(d) 63

Solution 73

Correct option: (a)

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

Question 74

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 74

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

Question 75

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 75

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)

e is an irrational number.

Π is an irrational number.

 

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

The sum of a rational number and an irrational number 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

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 78

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

Question 79

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 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

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

 

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

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 81

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

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

Solution 2

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

Question 3

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

Solution 3

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

Question 4

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

Solution 4

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

Question 5

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

Solution 5

Given, a = 1 and b = 2

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

Question 6

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

Solution 6

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

Question 7

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

Solution 7

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

Question 8

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

Solution 8

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 9

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

Solution 9

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

Question 10

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

Solution 10

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 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 

Question 12

Solve 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

Simplify 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

If 10x = 64, find the value of 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

Evaluate 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

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

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

Solution 17

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 18

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

Solution 18

(1296)0.17× (1296)0.08

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

Question 19

Simplify 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

Find an irrational number between 5 and 6.

Solution 20

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

Question 21

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

Rationalise 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

Solve for x: 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