Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$
$0.5 \overline{7}$
Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$
$0.5 \overline{7}$
Let, $x=0.5 \overline{7}$
$\therefore x=0.577 \ldots$ $....(1)$
Now, multiplying both the sides by $10.$
$10 x=5.77 \ldots$ $...(2)$
Subtract $(1)$ from $(2).$
$10 x=5.77 \ldots$
$\frac{-x=0.57\cdots}{9 x=5.2}$
$\therefore x=\frac{5.2}{9}=\frac{52}{90}=\frac{26}{45}$
Thus, $0.5 \overline{7}=\frac{26}{45}$
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