## Chapter 1 - Irrational Numbers Exercise 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)
Solution 14

(vi)
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 Exercise 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 numberon the number line.
Solution 36

## Chapter 1 - Irrational Numbers Exercise 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