UPSC Prelims 2020·CSAT·Quantitative Aptitude·Number System

The recurring decimal representation 1.272727... is equivalent to

Dalvoy logo
Reviewed by Dalvoy
UPSC Civil Services preparation
Last updated 23 May 2026, 3:31 pm IST
  1. A13/11
  2. B14/11Correct
  3. C127/99
  4. D137/99

Explanation

To convert a recurring decimal to a fraction, follow these steps: 1. Let x equal the given recurring decimal: x = 1.272727... (Equation 1) 2. Identify the repeating part. Here, '27' is the repeating block. Since there are two digits in the repeating block, multiply Equation 1 by 100: 100x = 127.272727... (Equation 2) 3. Subtract Equation 1 from Equation 2: 100x - x = 127.272727... - 1.272727... 99x = 126 4. Solve for x: x = 126 / 99 5. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9: x = (126 ÷ 9) / (99 ÷ 9) x = 14 / 11 Therefore, 1.272727... is equivalent to 14/11. Analyzing the options: A) 13/11 = 1.181818... (Incorrect) B) 14/11 = 1.272727... (Correct) C) 127/99 = 1.282828... (Incorrect) D) 137/99 = 1.383838... (Incorrect) The final answer is B.
Quantitative Aptitude: The recurring decimal representation 1.272727... is equivalent to

Related questions

More UPSC Prelims practice from the same subject and topic.