A) \[\frac{2355}{999}\]
B) \[\frac{2355}{1000}\]
C) \[\frac{2355}{1111}\]
D) None of these
Correct Answer: A
Solution :
Now,\[2.\overline{357}=2+0.357357357...\] \[\Rightarrow \] \[2.\overline{357}=2+0.357+0.000357+...\] \[\Rightarrow \] \[2.\overline{357}=2+\frac{357}{{{10}^{3}}}+\frac{357}{{{10}^{6}}}+...\] \[\Rightarrow \] \[2.\overline{357}=2+\frac{\frac{357}{{{10}^{3}}}}{1-\frac{1}{{{10}^{3}}}}\] \[=2+\frac{357}{999}\] \[\Rightarrow \] \[2.\overline{357}=\frac{2355}{999}\]
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