Question

Express $1.1\overline{43}$ in the form $\frac{p}{q}$ where $p$ and $q$ are integers, $q\ne 0$.

Answer 1

Let $x=1.1\overline{43}$,

then, $10x=11.\overline{43}$......(1)

$=11.43\overline{43}$

and $1000x=1143.\overline{43}$.......(2)

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

$990x=1132$

$\Rightarrow x=\frac{1132}{990}=\frac{566}{495}$