Question

Express $0.\overline{975}$ in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$.

Answer 1

Let $x=0.975$

As there are $3$ numbers under bar, multiply by $1000$

$\begin{array}{c}\Rightarrow 1000\times x=1000\times 0.975\\ \Rightarrow 1000x=975.975\end{array}$

Now, subtract $x$ from both sides

$1000x=975.975$

$x=0.975$

$999x=975.000$[bar cancel]

Reduce that and we get $\frac{39}{40}$