Question

Show that 1.272727..... can be expressed in the form of $\frac{p}{q}$, where p and q are integers and q $\ne$ 0

Answer 1

Let $x=1.272727$

$x=1.2\overline{7}$ …………$\left(1\right)$

Multiply equation $\left(1\right)$ by $100$

$100x=127.2727$

$100x=127.\overline{27}$ …………$\left(2\right)$

Substracting equation $\left(2\right)$ by equation $\left(1\right)$

$\therefore 99x=126.0000$

$\Rightarrow$$x=\frac{126}{99}$

$\therefore 1.2727$ can be expressed in form $\frac{p}{q}$ as $\frac{126}{99}$.