Question

The value of $0.\overline{2}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$ is :

• A. $\frac{1}{5}$
• B. $\frac{2}{9}$
• C. $\frac{2}{5}$
• D. $\frac{1}{8}$

Answer 1

Answer: (B)

$\frac{2}{9}$

let $x=0.\overline{2}=\mathrm{0.22222......}$

then $10x=\mathrm{2.2222222......}$

$\Rightarrow 10x-x=\mathrm{2.2222....}-0.222222$

$\Rightarrow 9x=2$

$\Rightarrow x=\frac{2}{9}$

So correct answer is option B