Convert $0.\overline{3}$ into $\frac{p}{q}$ form.

To Do: The representation of $0.3$ in $\frac{p}{q}$ form.

Let us consider $x=0.33333$ ......... $( i)$

$\Rightarrow 10x=3.3333$ ......... $( ii)$    [On multiplying by $10$ both sides]

Subtract equation $( i)$ from equation $( ii)$, we get

$10x-x=3.3333-0.3333$

$9x=3$

$x=\frac{3}{9}=\frac{1}{3}$

The representation of $0.3$ in $\frac{p}{q}$ form is $\frac{1}{3}$.