Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$

$0 . \overline{125}$

Let, $x=0 . \overline{125}$

$\therefore x=0.125125 \ldots$        $\ldots \ldots(1)$

Multiplying both the sides by $1000 .$

$1000 x=125.125 \ldots$         $.......(2)$

Subtract $(1)$ from $(2).$

$1000 x=125.125 \ldots$

$\frac{-x=0.125 \cdots}{999 x=125}$

$\therefore x=\frac{125}{999}$

Thus, $0 . \overline{125}=\frac{125}{999}$