Question

The value of $0.\overline{05}$ is equal to

• A. $\frac{3}{99}$
• B. $\frac{4}{99}$
• C. $\frac{5}{99}$
• D. None of these

Answer 1

The correct option is C $\frac{5}{99}$

$0.\overline{05}=\mathrm{0.05050505......}$

Let $x=\mathrm{0.0505050505......}$ $\left(1\right)$

Multiply equation $1$ by $100,$ we get

$100x=\mathrm{05.050505050505..........}$ $\left(2\right)$

Now subtracting equation $1)$ from equation $2),$ we get

$99x=5$

$\therefore x=\frac{5}{99}$