RD Sharma Solutions Class 9 Number System Exercise 1.3

RD Sharma Solutions Class 9 Chapter 1 Exercise 1.3

RD Sharma Class 9 Solutions Chapter 1 Ex 1.3 Free Download

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. \(\overline{37}\) = \(x = \frac{37}{99}\)