Convert the recurring decimal fraction 0.474747... (where 47 repeats infinitely) into a reduced vulgar fraction.
Answer and explanation
Correct answer: B. 47/99
- Step 1: Let x = 0.4747... Then 100x = 47.4747... Step 2. Subtract equations: 100x - x = 47 => 99x = 47 => x = 47/99. Answer: 47/99. Why not the others: 47/100 is terminating 0.47; 47/90 corresponds to 0.5222...; 43/90 corresponds to 0.4777... with only 7 recurring.
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