# FRANK Solutions for Class 9 Maths Chapter 1 - Irrational Numbers

In the Frank Solutions for ICSE Class 9 Mathematics Chapter 1 Irrational Numbers, understand the steps to place the given rational numbers in the ascending order. Find out how to determine whether the given number is rational or irrational.

Also, practise simplifying the given expression by using the technique of rationalising the denominator. Learn all this and more through TopperLearning’s Frank textbook solutions. To ensure a good grasp of irrational numbers, explore ICSE Class 9 Maths resources like videos, practice question papers and more.

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## Chapter 1 - Irrational Numbers Exercise Ex. 1.1

Question 1(a)

State which of these fractions have a terminating decimal.

Solution 1(a)

Question 1(b)

State which of these fractions have a terminating decimal.

Solution 1(b)

Question 1(c)

State which of these fractions have a terminating decimal.

Solution 1(c)

Question 1(d)

State which of these fractions have a terminating decimal.

Solution 1(d)

Question 1(e)

State which of these fractions have a terminating decimal.

Solution 1(e)

Question 1(f)

State which of these fractions have a terminating decimal.

Solution 1(f)

Question 1(g)

State which of these fractions have a terminating decimal.

Solution 1(g)

Question 1(h)

State which of these fractions have a terminating decimal.

Solution 1(h)

Question 1(i)

State which of these fractions have a terminating decimal.

Solution 1(i)

Question 2(a)

Express each of the following decimals as a rational number.

0.93

Solution 2(a)

Question 2(b)

Express each of the following decimals as a rational number.

4.56

Solution 2(b)

Question 2(c)

Express each of the following decimals as a rational number.

0.614

Solution 2(c)

Question 2(d)

Express each of the following decimals as a rational number.

21.025

Solution 2(d)

Question 3

(vi)

Solution 3

(vi)

Question 4(a)

Express each of the following decimals as a rational number.

Solution 4(a)

Question 4(b)

Express each of the following decimals as a rational number.

Solution 4(b)

Question 4(c)

Express each of the following decimals as a rational number.

Solution 4(c)

Question 4(d)

Express each of the following decimals as a rational number.

Solution 4(d)

Question 4(e)

Express each of the following decimals as a rational number.

Solution 4(e)

Question 4(f)

Express each of the following decimals as a rational number.

Solution 4(f)

Question 4(g)

Express each of the following decimals as a rational number.

Solution 4(g)

Question 4(h)

Express each of the following decimals as a rational number.

Solution 4(h)

Question 4(i)

Express each of the following decimals as a rational number.

Solution 4(i)

Question 5(b)

Insert a rational number between:

Solution 5(b)

Question 5(c)

Insert a rational number between:

Solution 5(c)

Question 5(d)

Insert a rational number between:

Solution 5(d)

Question 5(a)

Insert a rational number between:

Solution 5(a)

Question 6(a)

Insert a rational number between:

3 and 4

Solution 6(a)

Question 6(b)

Insert a rational number between:

7.6 and 7.7

Solution 6(b)

Question 6(c)

Insert a rational number between:

8 and 8.04

Solution 6(c)

Question 6(d)

Insert a rational number between:

101 and 102

Solution 6(d)

Question 7(a)

Insert three rational numbers between:

0 and 1

Solution 7(a)

Question 7(b)

Insert three rational number between:

6 and 7

Solution 7(b)

Question 7(c)

Insert three rational number between:

-3 and 3

Solution 7(c)

Question 7(d)

Insert three rational number between:

-5 and -4

Solution 7(d)

Question 8(a)

Insert five rational number between:

Solution 8(a)

Question 8(b)

Insert five rational number between:

Solution 8(b)

Question 9(a)

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

Solution 9(a)

Question 9(b)

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

Solution 9(b)

Question 10(a)

Arrange the following rational numbers in ascending order.

Solution 10(a)

Question 10(b)

Arrange the following rational numbers in ascending order.

Solution 10(b)

Question 10(c)

Arrange the following rational numbers in ascending order.

Solution 10(c)

Question 10(d)

Arrange the following rational numbers in ascending order.

Solution 10(d)

Question 11(a)

Arrange the following rational numbers in descending order.

Solution 11(a)

Question 11(b)

Arrange the following rational numbers in descending order.

Solution 11(b)

Question 11(c)

Arrange the following rational numbers in descending order.

Solution 11(c)

Question 11(d)

Arrange the following rational numbers in descending order.

Solution 11(d)

Question 12(a)

Find the value of:

Solution 12(a)

Question 12(b)

Find the value of:

Solution 12(b)

Question 12(c)

Find the value of:

Solution 12(c)

Question 12(d)

Find the value of:

Solution 12(d)

## Chapter 1 - Irrational Numbers Exercise Ex. 1.2

Question 1(a)

State, whether the following numbers are rational or irrational:

Solution 1(a)

Question 1(b)

State, whether the following numbers are rational or irrational:

Solution 1(b)

Question 1(c)

State, whether the following numbers are rational or irrational:

Solution 1(c)

Question 1(d)

State, whether the following numbers are rational or irrational:

Solution 1(d)

Question 2(a)

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

Solution 2(a)

Question 2(b)

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

Solution 2(b)

Question 2(c)

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

Solution 2(c)

Question 2(d)

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

Solution 2(d)

Question 3

Solution 3

Question 4

Solution 4

Question 5(a)

Write a pair of irrational numbers whose sum is irrational.

Solution 5(a)

Question 5(b)

Write a pair of irrational numbers whose sum is rational.

Solution 5(b)

Question 5(c)

Write a pair of irrational numbers whose difference is irrational.

Solution 5(c)

Question 5(d)

Write a pair of irrational numbers whose difference is rational.

Solution 5(d)

Question 5(e)

Write a pair of irrational numbers whose product is irrational.

Solution 5(e)

Question 5(f)

Write a pair of irrational numbers whose product is rational.

Solution 5(f)

Question 6(a)

Compare the following:

Solution 6(a)

Question 6(b)

Compare the following:

Solution 6(b)

Question 7(a)

Write the following in ascending order:

Solution 7(a)

Question 7(b)

Write the following in ascending order:

Solution 7(b)

Question 7(c)

Write the following in ascending order:

Solution 7(c)

Question 7(d)

Write the following in ascending order:

Solution 7(d)

Question 8(a)

Write the following in descending order:

Solution 8(a)

Question 8(b)

Write the following in descending order:

Solution 8(b)

Question 8(c)

Write the following in descending order:

Solution 8(c)

Question 9

Insert two irrational numbers between 3 and 4.

Solution 9

Question 10

Solution 10

Question 11

Write two rational numbers between and

Solution 11

Question 12

Write four rational numbers between and.

Solution 12

Question 13(a)

State which of the following are surds. Give reasons.

Solution 13(a)

Question 13(b)

State which of the following are surds. Give reasons.

Solution 13(b)

Question 13(c)

State which of the following are surds. Give reasons.

Solution 13(c)

Question 13(d)

State which of the following are surds. Give reasons.

Solution 13(d)

Question 13(e)

State which of the following are surds. Give reasons.

Solution 13(e)

Question 13(f)

State which of the following are surds. Give reasons.

Solution 13(f)

Question 14

Represent the numberon the number line.

Solution 14

## Chapter 1 - Irrational Numbers Exercise Ex. 1.3

Question 1(a)

Simplify by rationalising the denominator in each of the following:

Solution 1(a)

Question 1(b)

Simplify by rationalising the denominator in each of the following:

Solution 1(b)

Question 1(c)

Simplify by rationalising the denominator in each of the following:

Solution 1(c)

Question 1(d)

Simplify by rationalising the denominator in each of the following:

Solution 1(d)

Question 1(e)

Simplify by rationalising the denominator in each of the following:

Solution 1(e)

Question 1(f)

Simplify by rationalising the denominator in each of the following:

Solution 1(f)

Question 1(g)

Simplify by rationalising the denominator in each of the following:

Solution 1(g)

Question 1(h)

Simplify by rationalising the denominator in each of the following:

Solution 1(h)

Question 1(i)

Simplify by rationalising the denominator in each of the following:

Solution 1(i)

Question 2
Solution 2

Question 3
Solution 3
Question 4
Solution 4

Question 5

Solution 5

Question 6(a)

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

Solution 6(a)

Question 6(b)

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

Solution 6(b)

Question 6(c)

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

Solution 6(c)

Question 6(d)

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

Solution 6(d)

Question 6(e)

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

Solution 6(e)

Question 6(f)

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

Solution 6(f)

Question 6(g)

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

Solution 6(g)

Question 6(h)

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

Solution 6(h)

Question 6(i)

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

Solution 6(i)

Question 6(j)

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

Solution 6(j)

Question 7

(iv)

Solution 7

(iv)

Question 8

(v)

Solution 8

(v)

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

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