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Convert $0.\overline{3}$ into $\frac{p}{q}$ form.
To Do: The representation of $0.3$ in $\frac{p}{q}$ form.
Solution:
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 $\frac{1}{3}$.
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