A) \[\frac{232}{990}\]
B) \[\frac{232}{9990}\]
C) \[\frac{232}{990}\]
D) \[\frac{232}{9909}\]
Correct Answer: A
Solution :
\[0.\overset{\,\,\,\bullet \,\,\bullet }{\mathop{234}}\,=0.2343434.....\] =\[\therefore \] =\[0.2+\frac{34}{1000}+\frac{34}{100000}+\frac{34}{10000000}+.....\infty \] \[=\frac{2}{10}+34\left[ \frac{1}{{{10}^{3}}}+\frac{1}{{{10}^{5}}}+\frac{1}{{{10}^{7}}}+........\infty \right]\] \[=\frac{2}{10}+34\left[ \frac{1/{{10}^{3}}}{1-1/1000} \right]=\frac{2}{10}+34\times \frac{1}{1000}\times \frac{100}{99}\] \[=\frac{2}{10}+\frac{34}{990}=\frac{232}{990}\].
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