Question
Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$$0.\overline{47}$
✓
Answer
$0.\overline{47}=0.4777...$Let $\text{x}=0.4777 \ ...\text{(i)}$
$10\text{x}=4.777$
$100\text{x}=47.777 \ ...(\text{ii})$
(ii) - (i) gives
$99\text{x}=43$
$\text{x}=\frac{43}{99}$
$10\text{x}=4.777$
$100\text{x}=47.777 \ ...(\text{ii})$
(ii) - (i) gives
$99\text{x}=43$
$\text{x}=\frac{43}{99}$
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