Question

The value of $0.0\overline{37}$, where $0.0\overline{37}$ stands for the number $0.0373737\dots$ is

• A. $\frac{37}{1000}$
• B. $\frac{37}{990}$
• C. $\frac{1}{37}$
• D. $\frac{1}{27}$

Answer 1

The correct option is B

$\frac{37}{990}$

Explanation for correct option

Let$x=0.0373737\dots$

$$\begin{gathered} 1000x=37.3737\dots . \\ \Rightarrow 10x=0.3737\dots \\ \Rightarrow 1000x–10x=37 \\ \Rightarrow 990x=37 \\ \Rightarrow x=\frac{37}{990} \end{gathered}$$

Hence $\mathrm{Option}\left(\mathrm{B}\right)$ is the answer.