Question

Express $1.3\overline{23}$ in the form $\frac{p}{q}$ where $p$ and $q$ are integers, $q\ne 0$.

Answer 1

Let, $x=1.3\overline{23}$.

Then, $10x=13.\overline{23}$........(1)

$=13.23\overline{23}$

and $1000x=1323.\overline{23}$........(2)

Now, subtracting (1) from (2) we get,

$990x=1310$

$\Rightarrow x=\frac{1310}{990}=\frac{131}{99}$

Which is the required $\frac{p}{q}$ form.