Exercise 1.1

1. (a) Write any three rational numbers

Solution:

12−1,

−34−5,

0−2

1. (b) Explain rational number in your own words.

Solution:

A rational number is any number that cancan't be expressed as a fraction pq, where p and q are , and q is not .

2. Give one example each to the following statements.

i. A number which is rational but not an integer

Solution:

122

ii. A whole number which is not a natural number

Solution:

iii. An integer which is not a whole number

Solution:

-11

iv. A number which is natural number, whole number, integer and rational number.

Solution:

112

v. A number which is an integer but not a natural number.

Solution:

-55

3. Find five rational numbers between 1 and 2.

Solution:

Since 1 = 66 and 2 = 126

Therefore five rational numbers between 1 and 2 are: 7672,

86174,

9692,

106103,

116114

4. Insert three rational numbers between 3/5 and 2/3.

Solution:

First, find a common denominator for 35 and 23.The least common denominator is .

35 = 915315

23 = 1015215

To insert three rational numbers, we can use a larger denominator.

Let's multiply by 4 = 15 × 4 = :

35 = 3660960

23 = 40601060

So the three rational numbers between 35 and 23 are:

= 37603730,

= 38603740,

= 39603750.

5. Represent 8/5 and -8/5 on the number line.

Solution:

−85 lies in between -1.5-2 and -1-2 while 85 lies in between and .

6. Express the following rational numbers in decimal form.

i. 2421000

Solution:

ii. 354500

Solution:

iii. 25

Solution:

iv. 1154

Solution:

v. 23

Solution:

... (give upto 3 decimal values)

vi. −2536

Solution:

... (give upto 4 decimal values).

vii. 227

Solution:

(give upto 3 decimal values)

viii. 119

Solution:

... (give upto 3 decimal values).

7. Express each of the following decimals in p/q form where q ≠ 0 and p, q are integers.

i. 0.36

Solution:

925825

ii. 15.4

Solution:

775645

iii. 10.25

Solution:

414434

iv. 3.25

Solution:

134154

8. Express each of the following decimal numbers in pq form.

i. 0.5

Solution:

ii. 3.8

Solution:

iii. 0.36

Solution:

iv. 3.127

Solution:

9. Without actually dividing find which of the following are terminating decimals.

(i) 325

Solution:

The rational number is a terminating decimal: YesNo

325 = 35×5

The denominator is the factor of only .

Therefore, the rational number is a terminating decimal.

(ii) 1118

Solution:

The rational number is a terminating decimal: NoYes

1118 = 112×3×3

The denominator is not the only factor of only 2 or or both.

Therefore, the rational number is a non-terminatingterminating decimal.

(iii) 1320

Solution:

The rational number is a terminating decimal: YesNo

1320 = 132×5×2

The denominator is the only factor of only or or both.

Therefore, the rational number is a decimal.

(iv) 4142

Solution:

The rational number is a terminating decimal: NoYes

4142 = 412×3×7

The denominator is not the only factor of only 2 or 5.

Therefore the rational number is a non-terminatingterminating decimal.