Question

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

• A. $\frac{14}{9}$
• B. $\frac{35}{99}$
• C. $\frac{14}{13}$
• D. $\frac{14}{15}$

Answer 1

The correct option is B

$\frac{35}{99}$

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

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

Multiply both sides of (1) by 100

to get 100x = 35.3535.. ------(2)

Subtracting (1) from (2), we get

100x - x = (35.35353 ...) - (0.3535...)

$\Rightarrow$ 99x = 35

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