Question

Convert each of the following recuring decimals in to a vulgar fraction.
$0.\overline{4}$.

Answer 1

Let $x=$$0.\overline{4}$

or, $x=\mathrm{0.4444......}$

or, $x=0.4\overline{4}$.....(1).

or, $10x=4.\overline{4}$.....(2).

Now (2)-(1) we get,

$9x=4$

or, $x=\frac{4}{9}$.

This is the required fraction.