Question

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

• A. $\frac{1}{11}$
• B. $\frac{2}{11}$
• C. $\frac{3}{11}$
• D. $\frac{4}{11}$

Answer 1

The correct option is B

$\frac{2}{11}$

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 =18.1818.... - 0.1818......

$\Rightarrow$ 99x = 18

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