Question

Express the following in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$
$0.4\overline{7}$

Answer 1

Let $x=0.4\overline{7}$

$10x=4.\overline{7}=4.7\overline{7}$

$10x=4.3+x$

$9x=4.3$ $=\frac{43}{10}$

$\Rightarrow x=\frac{43}{90}$