Question

Express the following in form of $\frac{p}{q}$

a)$0.\overline{47}$

Answer 1

$0.\overline{47}$

let $x=0.\overline{47}=\mathrm{0.474747..}-\left(1\right)$

Multiply by $100$

$100x=\mathrm{47.4747...}-\left(2\right)$

Subtract $\left(1\right)$ from $\left(2\right)$

$\Rightarrow (100x-x)=\mathrm{47.4747....}-\mathrm{0.474747...}$

$\Rightarrow 99x=47$

$\Rightarrow x=\frac{47}{99}$