Question

Express $0.00\overline{32}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

Answer 1

Let $x=\mathrm{0.00323232..}$

Multiplying (1) by $100$ and $10000$ successively, we get
Then $100x=0.323232\dots \dots$(1)
and $10000x=32.323232...$(2)
Subtracting (1) from (2),

$10000x-100x=32.323232-0.323232$

we get
$9900x=32$
$\Rightarrow x=\frac{32}{9900}$
$\Rightarrow x=\frac{8}{2475}$

Thus, $0.00323232$