Question

Express the decimals in the from of $\frac{p}{q}$ :
$125.\overline{3}$

Answer 1

Let $y=125.\overline{3}...............\left(1\right)$
Multiplying $10$ on both sides, we get
$\Rightarrow 10y=1253.\overline{3}...............\left(2\right)$

Subtracting (1) from (2)
$\Rightarrow 10y-y=1253.\overline{3}-125.\overline{3}$

$\Rightarrow 9y=1128$
$\Rightarrow y=\frac{1128}{9}$
$\therefore y=\frac{376}{3}$