Question

Express $1.\overline{137}$ as a fraction.

Answer 1

Express $1.\overline{137}$ as fraction.

$x=\mathrm{1.137137137...}\dots \dots$ ……$\left(1\right)$

$1000x=\mathrm{1137.137137...}\dots$ ……..$\left(2\right)$

$\left(2\right)-\left(1\right)$

$\Rightarrow 999x=\left(\mathrm{1137.137137.....}\right)-\left(\mathrm{1.137137....}\right)$

$999x=1136$

$x=\frac{1136}{999}$.