Q. The value of $2.\overline{357}$ is
A) $\frac{2355}{999}$
B) $\frac{2355}{1000}$
C) $\frac{2355}{1111}$
D) None of these
Explanation
(a)
$2.\overline{357} = 2 + 0.357 + 0.000357 + ...$
$\Rightarrow \ 2.\overline{357} = 2 + \frac{357}{10^{3}} + \frac{357}{10^{6}} + ...$
$\Rightarrow \ 2.\overline{357} = 2 + \frac{\frac{357}{10^{3}}}{1 - \frac{1}{10^{3}}} = 2 + \frac{357}{999} = \frac{2355}{999}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.