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

Let $x=0.\overline{2}=\mathrm{0.222...}$ -----(1)

Multiplying both sides by 10, we get

$10x=\mathrm{2.2222...}$----- (2)

Subtracting (1) from (2), we get

$10x-x=\mathrm{2.222...}-\mathrm{0.2222..}\Rightarrow 9x=2\Rightarrow x=\frac{2}{9}\therefore 0.\overline{2}=\frac{2}{9}$

Hence, the correct answer is the option (b).