Question

Express each of the following as a fraction in simplest form :$0.3\overline{65}$

Answer 1

$x=0.3\overline{65}$

then,
$x=\mathrm{0.3656565.}-------\left(1\right)$
$\therefore 10x=\mathrm{3.656565..}--------\left(2\right)$
$1000x=365.656565.....------\left(3\right)$

On subtracting (2) from (3) we get,
$990x=362$ x = \dfrac {362}{990} = \dfrac {181}{495} $

$0.3\overline{65}=\frac{181}{495}$