The recurring decimal representation 1·272727... is equivalent to
- (a) 13/11
- (b) 14/11 ✓ UPSC's answer
- (c) 127/99
- (d) 137/99
Why the answer is (b)
• Let x = 1.272727..., where the digits '27' repeat indefinitely.
• Since the repeating block has two digits, multiply x by 100 to shift the decimal point: 100x = 127.272727...
• Subtract the original equation (x = 1.272727...) from the new equation: 100x - x = 127.272727... - 1.272727...
• This simplifies to 99x = 126.
• Solving for x gives x = 126/99, which simplifies to 14/11 by dividing numerator and denominator by 9.
Why the other options are wrong
- (a) 13/11
- 13/11 equals 1.1818..., which does not match the repeating decimal 1.2727....
- (c) 127/99
- 127/99 equals 1.2828..., which is incorrect because the numerator should be 126, not 127.
- (d) 137/99
- 137/99 equals 1.3838..., which is significantly higher than the target value of 1.2727...
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.