Question

$0.\overline{27}$ in $\frac{p}{q}$ form is ___________ ,

Answer 1

Representing $0.\overline{27}$ in the form of $\frac{p}{q}$:

We are given a number $0.\overline{27}$.

We need to write it in $\frac{p}{q}$ form.

So, let $x=0.\overline{27}$

$x=0.272727..............$------------------------(1)

Two digits $27$are repeating. So,

Multiplying by 100 on both sides, we get

$\Rightarrow 100x=27.2727................$ -----------------------(2)

Subtracting (1) from (2), we get

$\Rightarrow 99x=27$

$\Rightarrow x=\frac{27}{99}$

$\Rightarrow x=\frac{3}{11}$

Hence, given number $0.\overline{27}$ in $\frac{p}{q}$ the form is $\frac{3}{11}$.