# RD Sharma Solutions Class 9 Number System Exercise 1.3

## RD Sharma Solutions Class 9 Chapter 1 Ex 1.3

Q1. Express each of the following decimals in the form of rational number.

(i)   0.39

(ii)  0.750

(iii) 2.15

(iv) 7.010

(v)  9.90

(vi) 1.0001

Solution:

(i)   Given,

0.39 = $\frac{39}{100}$

(ii) Given,

0.750 = $\frac{750}{1000}$

(iii) Given,

2.15 = $\frac{215}{100}$ (iv) Given,9.101

(iv)  Given,

7.010 = $\frac{7010}{1000}$

(v) Given,

9.90 = $\frac{990}{100}$

(vi) Given,

1.0001 = $\frac{10001}{10000}$

Q2. Express each of the following decimals in the form of rational number ($\frac{p}{q}$)

(i) 0. $\overline{4}$

(ii) 0. $\overline{37}$

Solution:

(i) Let x = 0. $\overline{4}$

Then, x = 0. $\overline{4}$ = 0.444…        ___ (a)

Multiplying both sides of equation (a) by 10, we get,

10x = 4.44….                                                                ___ (b)

Subtracting equation (1) by (2)

9x = 4

$x = \frac{4}{9}$

Hence, 0. $\overline{4}$ = $x = \frac{4}{9}$

(ii) Let x = 0. $\overline{37}$

Then, x = 0. $\overline{37}$ = 0.3737…        ___ (a)

Multiplying both sides of equation (a) by 100, we get,

100 x = 37.37….                                                                ___ (b)

Subtracting equation (1) by (2)

99 x = 37

$x = \frac{37}{99}$

Hence, 0. $\overline{37}$ = $x = \frac{37}{99}$

#### Practise This Question

Observe the pattern given below

1,4,9,16,25......

The term at nth position will be given by expression