Question:
The fractional value of 2.357 is
(a) 2355/1001
(b) 2379/997
(c) 2355/999
(d) none of these
Solution:
(C) $\frac{2355}{999}$
$2 . \overline{357}=2.0+0.357+0.000357+0.000000357+\ldots \infty$
$\Rightarrow 2 . \overline{357}=2+\left[\frac{357}{10^{3}}+\frac{357}{10^{6}}+\frac{357}{10^{9}}+\ldots \infty\right]$
$\Rightarrow 2 . \overline{357}=2+\frac{\frac{357}{10^{3}}}{1-\frac{1}{10^{2}}}$
$\Rightarrow 2 . \overline{357}=2+\frac{357}{999}$
$\Rightarrow 2 . \overline{357}=\frac{2355}{999}$
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