Question
Express the following decimals in the form $\frac{\text{p}}{\text{q}},$ where $p, q$ are integers and $\text{q}\neq0.$ $0.00\overline{32}$

Answer

$0.00\overline{32}$
 Let $x = 0.003232 ...(i)$
we multiply $x$ by $100. 100x = 0.3232 ...(ii)$
Again multiplying by $100$ as there are $2$ repeating numbers after decimals
we get $10000x = 32.3232 ...(iii)$
Subtracting $(ii)$ from $(iii)$
we get $9900x = 32$ 
 $\Rightarrow\text{x}=\frac{32}{9900}=\frac{8}{2475}$

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