Question

The $\frac{p}{q}$ form of $0.\overline{18}$ is (where p and q are integers and $q\ne 0$) .

• A. $\frac{2}{11}$
• B. $\frac{2}{22}$
• C. $\frac{2}{33}$

Answer 1

The correct option is A $\frac{2}{11}$

Given decimal is 0.181818......

Let us assume,

$x=0.181818$........ ---(1)

Multiply both sides of (1) by 100

$\therefore 100x$ = 18.1818.... ---(2)

Subtracting (1) from (2), we get $100x-x=\mathrm{18.1818....}-\mathrm{0.1818......}$

$\Rightarrow 99x=18$ $\Rightarrow \text{x}=\frac{18}{99}=\frac{2}{11}$
$\therefore \frac{p}{q}$ form of the given decimal is $\frac{2}{11}$.