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Question
The fractional value of 2.357 is
Options
(a) 2355/1001
(b) 2379/997
(c) 2355/999
(d) none of these
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Solution
(c) \[\frac{2355}{999}\]
\[2 . \bar{{357}} = 2 . 0 + 0 . 357 + 0 . 000357 + 0 . 000000357 + . . . \infty \]
\[ \Rightarrow 2 . \bar{{357}} = 2 + \left[ \frac{357}{{10}^3} + \frac{357}{{10}^6} + \frac{357}{{10}^9} + . . . \infty \right]\]
\[ \Rightarrow 2 . \bar{{357}} = 2 + \frac{\frac{357}{{10}^3}}{1 - \frac{1}{{10}^3}}\]
\[ \Rightarrow 2 . \bar{{357}} = 2 + \frac{357}{999}\]
\[ \Rightarrow 2 . \bar{{357}} = \frac{2355}{999}\]
\[\]
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