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The value of

Question:

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

(a) $\frac{1}{5}$

(b) $\frac{2}{9}$

(c) $\frac{2}{5}$

(d) $\frac{1}{8}$

Solution:

Let $x=0 . \overline{2}=0.222 \ldots \quad \ldots$ (1)

Multiplying both sides by 10, we get

$10 x=2 . \overline{2} \quad \ldots \ldots(2)$

Subtracting (1) from (2), we get

$10 x-x=2 . \overline{2}-0 . \overline{2}$

$\Rightarrow 9 x=2$

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

 

$\therefore 0 . \overline{2}=\frac{2}{9}$

Hence, the correct answer is option (b).

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