Question

The fractional value of 2.357 is
(a) 2355/1001
(b) 2379/997
(c) 2355/999
(d) none of these

Answer 1

(c)$\frac{2355}{999}$

$$\begin{gathered} 2.\overline{357}=2.0+0.357+0.000357+0.000000357+...\infty \\ \Rightarrow 2.\overline{357}=2+\left[\frac{357}{{10}^3}+\frac{357}{{10}^6}+\frac{357}{{10}^9}+...\infty \right] \\ \Rightarrow 2.\overline{357}=2+\frac{\frac{357}{{10}^3}}{1-{\displaystyle \frac{1}{{10}^3}}} \\ \Rightarrow 2.\overline{357}=2+\frac{357}{999} \\ \Rightarrow 2.\overline{357}=\frac{2355}{999} \end{gathered}$$