Question

Express $3.\overline{2}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

Answer 1

Let $x=3.\overline{2}$ (Pure recurring decimal)
i.e. $x=3.2222......$(1)
Multiplying $\left(1\right)$ by $10$, we get
$10x=32.2222.......$(2)
Subtracting $\left(1\right)$ from $\left(2\right),$ we get
$10x-x=(32.222\dots )-(3.222\dots )$
$\Rightarrow 9x=29$
$\Rightarrow x=\frac{29}{9}$

Thus, $3.\overline{2}=\frac{29}{9}$