Question

The value of $0.0373737$..... is

• A. $\frac{37}{999}$
• B. $\frac{37}{99}$
• C. $\frac{37}{990}$
• D. $\frac{37}{1000}$

Answer 1

Answer: (C)

Let $x=0.0\overline{37}\Rightarrow 10x=0.\overline{37}$
$\Rightarrow 1000x=37.\overline{37}=37+0.\overline{37}=37+10x$
$\Rightarrow 990x=37\Rightarrow x=\frac{37}{990}$