Question

In the simplest $\frac{p}{q}$ form of $0.\overline{18}$, find p+q.

• A. 13

Answer 1

The correct option is A 13

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 $\frac{2}{11}$.
p+q = 2+11 = 13