Question

Express each of the following as a fraction in simplest form :$0.\overline{12}$

Answer 1

$x=0.1\overline{2}$ then,
$x=\mathrm{0.12222...}-------$
$\therefore 10x=\mathrm{1.2222...}--------\left(1\right)$
$100x=12.2222.....------\left(2\right)$
On subtracting (1) from (2) we get,
$90x=11$
$x=\frac{11}{90}$

$0.1\overline{2}=\frac{11}{90}$