# 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.

## Chapter 1 - Irrational Numbers Excercise Ex. 1.1

State which of these fractions have a terminating decimal.

State which of these fractions have a terminating decimal.

State which of these fractions have a terminating decimal.

State which of these fractions have a terminating decimal.

State which of these fractions have a terminating decimal.

State which of these fractions have a terminating decimal.

State which of these fractions have a terminating decimal.

State which of these fractions have a terminating decimal.

State which of these fractions have a terminating decimal.

Express each of the following decimals as a rational number.

0.93

Express each of the following decimals as a rational number.

4.56

Express each of the following decimals as a rational number.

0.614

Express each of the following decimals as a rational number.

21.025

(vi)

(vi)

Express each of the following decimals as a rational number.

Express each of the following decimals as a rational number.

Express each of the following decimals as a rational number.

Express each of the following decimals as a rational number.

Express each of the following decimals as a rational number.

Express each of the following decimals as a rational number.

Express each of the following decimals as a rational number.

Express each of the following decimals as a rational number.

Express each of the following decimals as a rational number.

Insert a rational number between:

Insert a rational number between:

Insert a rational number between:

Insert a rational number between:

Insert a rational number between:

3 and 4

Insert a rational number between:

7.6 and 7.7

Insert a rational number between:

8 and 8.04

Insert a rational number between:

101 and 102

Insert three rational numbers between:

0 and 1

Insert three rational number between:

6 and 7

Insert three rational number between:

-3 and 3

Insert three rational number between:

-5 and -4

Insert five rational number between:

Insert five rational number between:

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

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

Arrange the following rational numbers in ascending order.

Arrange the following rational numbers in ascending order.

Arrange the following rational numbers in ascending order.

Arrange the following rational numbers in ascending order.

Arrange the following rational numbers in descending order.

Arrange the following rational numbers in descending order.

Arrange the following rational numbers in descending order.

Arrange the following rational numbers in descending order.

Find the value of:

Find the value of:

Find the value of:

Find the value of:

## Chapter 1 - Irrational Numbers Excercise Ex. 1.2

State, whether the following numbers are rational or irrational:

State, whether the following numbers are rational or irrational:

State, whether the following numbers are rational or irrational:

State, whether the following numbers are rational or irrational:

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

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

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

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

Write a pair of irrational numbers whose sum is irrational.

Write a pair of irrational numbers whose sum is rational.

Write a pair of irrational numbers whose difference is irrational.

Write a pair of irrational numbers whose difference is rational.

Write a pair of irrational numbers whose product is irrational.

Write a pair of irrational numbers whose product is rational.

Compare the following:

Compare the following:

Write the following in ascending order:

Write the following in ascending order:

Write the following in ascending order:

Write the following in ascending order:

Write the following in descending order:

Write the following in descending order:

Write the following in descending order:

Insert two irrational numbers between 3 and 4.

Write two rational numbers between and

Write four rational numbers between and.

State which of the following are surds. Give reasons.

State which of the following are surds. Give reasons.

State which of the following are surds. Give reasons.

State which of the following are surds. Give reasons.

State which of the following are surds. Give reasons.

State which of the following are surds. Give reasons.

Represent the numberon the number line.

## Chapter 1 - Irrational Numbers Excercise Ex. 1.3

Simplify by rationalising the denominator in each of the following:

Simplify by rationalising the denominator in each of the following:

Simplify by rationalising the denominator in each of the following:

Simplify by rationalising the denominator in each of the following:

Simplify by rationalising the denominator in each of the following:

Simplify by rationalising the denominator in each of the following:

Simplify by rationalising the denominator in each of the following:

Simplify by rationalising the denominator in each of the following:

Simplify by rationalising the denominator in each of the following:

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

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

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

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

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

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

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

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

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

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

(iv)

(iv)

(v)

(v)

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