Question

Express in $\frac{p}{q}$ form $0.4\overline{7}$

Answer 1

Let $x=0.4\overline{7}10x=4.\overline{7}..............\left(1\right)100x=47.\overline{7}.............\left(2\right)$

Subtracting (1) from (2)

$100x-10x=47.\overline{7}-4.\overline{7}\Rightarrow 90x=43\Rightarrow x=\frac{43}{90}$