Question

$\text{Express the following in the form}$$\frac{p}{q}$, $\text{where p and q are integers and}q\ne 0$
(i) 0.00323232...
(ii) 0.404040…

Answer 1

(i) Let x = 0.00323232...
On multiplying the above equation by 100 we get
100x = 0.3232...
On multiplying the above equation by 100 we get
10000x = 32.3232...
$\therefore$ 10000x – 100x = (32.32...) - (0.3232…)
$\Rightarrow 9900x=32$
$\therefore x=\frac{32}{9900}=\frac{8}{2475}$ [ Dividing numerator and denominator by 4]

(ii) Let x=0.404040...
On Multiplying the above equation by 100, we get
100x=40.4040...
$\Rightarrow$100x-x=(40.4040...) - (0.404040...)
$\Rightarrow 99x=40$
$\therefore x=\frac{40}{99}$