Chapter 1 : Irrational Numbers - Frank Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

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Chapter 1 - Irrational Numbers Excercise Ex. 1.1

Question 1

State which of these fractions have a terminating decimal.

  

Solution 1

Question 2

State which of these fractions have a terminating decimal.

  

Solution 2

Question 3

State which of these fractions have a terminating decimal.

Solution 3

Question 4

State which of these fractions have a terminating decimal.

  

Solution 4

Question 5

State which of these fractions have a terminating decimal.

Solution 5

Question 6

State which of these fractions have a terminating decimal.

Solution 6

Question 7

State which of these fractions have a terminating decimal.

  

Solution 7

Question 8

State which of these fractions have a terminating decimal.

  

Solution 8

Question 9

State which of these fractions have a terminating decimal.

Solution 9

Question 10

Express each of the following decimals as a rational number.

0.93

Solution 10

Question 11

Express each of the following decimals as a rational number.

4.56

Solution 11

Question 12

Express each of the following decimals as a rational number.

0.614

Solution 12

Question 13

Express each of the following decimals as a rational number.

21.025

Solution 13

Question 14

(vi) begin mathsize 12px style 2 over 3 end style

Solution 14

(vi)

begin mathsize 12px style 2 over 3 equals 0.6666....... equals 0.6 with dot on top end style

Question 15

Express each of the following decimals as a rational number.

Solution 15

Question 16

Express each of the following decimals as a rational number.

Solution 16

Question 17

Express each of the following decimals as a rational number.

Solution 17

Question 18

Express each of the following decimals as a rational number.

  

Solution 18

Question 19

Express each of the following decimals as a rational number.

Solution 19

Question 20

Express each of the following decimals as a rational number.

Solution 20

Question 21

Express each of the following decimals as a rational number.

Solution 21

Question 22

Express each of the following decimals as a rational number.

  

Solution 22

Question 23

Express each of the following decimals as a rational number.

Solution 23

Question 24

Insert a rational number between:

Solution 24

Question 25

Insert a rational number between:

Solution 25

Question 26

Insert a rational number between:

Solution 26

Question 27

Insert a rational number between:

  

Solution 27

Question 28

Insert a rational number between:

3 and 4

Solution 28

Question 29

Insert a rational number between:

7.6 and 7.7

Solution 29

Question 30

Insert a rational number between:

8 and 8.04

Solution 30

Question 31

Insert a rational number between:

101 and 102

Solution 31

Question 32

Insert three rational numbers between:

0 and 1

Solution 32

Question 33

Insert three rational number between:

6 and 7

Solution 33

Question 34

Insert three rational number between:

-3 and 3

Solution 34

Question 35

Insert three rational number between:

-5 and -4

Solution 35

Question 36

Insert five rational number between:

Solution 36

Question 37

Insert five rational number between:

Solution 37

Question 38

Find the greatest and the smallest rational number among the following.

Solution 38

Question 39

Find the greatest and the smallest rational number among the following.

Solution 39

Question 40

Arrange the following rational numbers in ascending order.

Solution 40

Question 41

Arrange the following rational numbers in ascending order.

Solution 41

Question 42

Arrange the following rational numbers in ascending order.

  

Solution 42

Question 43

Arrange the following rational numbers in ascending order.

Solution 43

Question 44

Arrange the following rational numbers in descending order.

Solution 44

Question 45

Arrange the following rational numbers in descending order.

Solution 45

Question 46

Arrange the following rational numbers in descending order.

Solution 46

Question 47

Arrange the following rational numbers in descending order.

Solution 47

Question 48

Find the value of:

  

Solution 48

Question 49

Find the value of:

Solution 49

Question 50

Find the value of:

Solution 50

Question 51

Find the value of:

Solution 51

Chapter 1 - Irrational Numbers Excercise Ex. 1.2

Question 1

State, whether the following numbers are rational or irrational:

  

Solution 1

Question 2

State, whether the following numbers are rational or irrational:

  

Solution 2

Question 3

State, whether the following numbers are rational or irrational:

  

Solution 3

Question 4

State, whether the following numbers are rational or irrational:

  

Solution 4

Question 5

Check whether the square of the following is rational or irrational:

Solution 5

Question 6

Check whether the square of the following is rational or irrational:

Solution 6

  

Question 7

Check whether the square of the following is rational or irrational:

  

Solution 7

Question 8

Check whether the square of the following is rational or irrational:

Solution 8

Question 9

  

Solution 9

Question 10

  

Solution 10

Question 11

Write a pair of irrational numbers whose sum is irrational.

Solution 11

Question 12

Write a pair of irrational numbers whose sum is rational.

Solution 12

Question 13

Write a pair of irrational numbers whose difference is irrational.

Solution 13

Question 14

Write a pair of irrational numbers whose difference is rational.

Solution 14

Question 15

Write a pair of irrational numbers whose product is irrational.

Solution 15

Question 16

Write a pair of irrational numbers whose product is rational.

Solution 16

Question 17

Compare the following:

  

Solution 17

Question 18

Compare the following:

  

Solution 18

Question 19

Write the following in ascending order:

  

Solution 19

Question 20

Write the following in ascending order:

  

Solution 20

Question 21

Write the following in ascending order:

Solution 21

Question 22

Write the following in ascending order:

  

Solution 22

Question 23

Write the following in descending order:

  

Solution 23

Question 24

Write the following in descending order:

  

Solution 24

Question 25

Write the following in descending order:

Solution 25

Question 26

Insert two irrational numbers between 3 and 4.

Solution 26

Question 27

  

Solution 27

Question 28

Write two rational numbers between  and

Solution 28

Question 29

Write four rational numbers between  and .

Solution 29

Question 30

State which of the following are surds. Give reasons.

Solution 30

 

Question 31

State which of the following are surds. Give reasons.

  

Solution 31

Question 32

State which of the following are surds. Give reasons.

  

Solution 32

Question 33

State which of the following are surds. Give reasons.

  

Solution 33

Question 34

State which of the following are surds. Give reasons.

Solution 34

Question 35

State which of the following are surds. Give reasons.

  

Solution 35

Question 36

Represent the number on the number line.

Solution 36

  

 

Chapter 1 - Irrational Numbers Excercise Ex. 1.3

Question 1

Simplify by rationalising the denominator in each of the following:

Solution 1

Question 2

Simplify by rationalising the denominator in each of the following:

  

Solution 2

Question 3

Simplify by rationalising the denominator in each of the following:

  

Solution 3

Question 4

Simplify by rationalising the denominator in each of the following:

  

Solution 4

Question 5

Simplify by rationalising the denominator in each of the following:

  

Solution 5

Question 6

Simplify by rationalising the denominator in each of the following:

  

Solution 6

Question 7

Simplify by rationalising the denominator in each of the following:

  

Solution 7

Question 8

Simplify by rationalising the denominator in each of the following:

  

Solution 8

Question 9

Simplify by rationalising the denominator in each of the following:

  

Solution 9

Question 10
Solution 10

Question 11
Solution 11
Question 12
Solution 12

Question 13

  

Solution 13

Question 14

In each of the following, find the values of a and b:

Solution 14

Question 15

In each of the following, find the values of a and b:

Solution 15

Question 16

In each of the following, find the values of a and b:

Solution 16

Question 17

In each of the following, find the values of a and b:

Solution 17

Question 18

In each of the following, find the values of a and b:

Solution 18

Question 19

In each of the following, find the values of a and b:

Solution 19

Question 20

In each of the following, find the values of a and b:

Solution 20

Question 21

In each of the following, find the values of a and b:

Solution 21

Question 22

In each of the following, find the values of a and b:

Solution 22

Question 23

In each of the following, find the values of a and b:

  

Solution 23

Question 24

(iv)

Solution 24

(iv)

Question 25

(v)

Solution 25

(v)

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

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