Question

Express $\overline{1.27}$ in the form of $\frac{p}{q}$.

Answer 1

Express the given number in rational form

We know that $\overline{1.27}=1.2727272727...$

So, let $x=1.2727272727...$ $...\left(1\right)$

Multiply $100$ on both sides

$100x=127.27272727...$ $...\left(2\right)$

Subtract $\left(1\right)$ from $\left(2\right)$, we get

$$\begin{gathered} \Rightarrow 100x-x=127.27272727-1.27272727 \\ \Rightarrow 99x=126.0000 \\ \Rightarrow x=\frac{126}{99} \\ \Rightarrow x=\frac{14}{11} \end{gathered}$$

Therefore, $\overline{1.27}$ in the form of $\frac{p}{q}$ is $\frac{14}{11}$.