Question

The number $0.\overline{35}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$, is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let $x=0.\overline{35}$

$\Rightarrow x=\mathrm{0.353535....}-----\left(1\right)$

Multiply both sides of (1) by 100

to get $100x=\mathrm{35.3535..}------\left(2\right)$

Subtracting (1) from (2), we get

$100x-x=(35.35353...)-\left(\mathrm{0.3535...}\right)$

$\Rightarrow$ $99x=35$

$\Rightarrow x=\frac{35}{99}\text{Hence,}0.\overline{35}=\frac{35}{99}$