Question

Prove that the rational number which equals to the number $2.\overline{357}$ with recurring decimal is $\frac{2355}{999}$.

Answer 1

$x=2\cdot 357357357.$
$\therefore 1000x=2357\cdot 357357.$
Subtracting, $999x=2355$ $\therefore x=\frac{2355}{999}$ etc.