Question

Express $0.\overline{36}$ in the $\frac{p}{q}$ form.

Answer 1

Let $x=0.\overline{36}=0.3636$..........................$\left(1\right)$

Multiply (1) by 100 we get

$100x=36.3625$..............................................$\left(2\right)$

Substruct $\left(2\right)$ By $\left(1\right)$ we get

$99x=36$

$\Rightarrow x=\frac{36}{99}=\frac{12}{33}$