A) \[2.3\overline{100191}\]
B) \[2.3\overline{101091}\]
C) \[2.3\overline{110091}\]
D) \[2.3\overline{110901}\]
Correct Answer: A
Solution :
\[3.\overline{76}-1.4\overline{576}=3+0.\overline{76}-1-0.4\overline{576}\] \[=3+\left( \frac{76-0}{99} \right)-1-\left( \frac{4576-4}{9990} \right)\] \[=3+\frac{76}{99}-1-\frac{4572}{9990}\] \[=2+\left( \frac{76}{99}-\frac{4572}{9990} \right)\] \[=2+\frac{1}{9}\left( \frac{76}{11}-\frac{4572}{1110} \right)\] \[=2+\frac{1}{9}\times \frac{(84360-50292)}{12210}\] \[=2+\frac{1}{9}\times \frac{34068}{12210}\] \[=2+\frac{11356}{36630}\] \[=2+0.3\overline{100191}\] \[=2.3\overline{100191}\]
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