Q. The recurring decimal representation 1.272727… is equivalent to
(a) 13/11
(b) 14/11
(c) 127/99
(d) 137/99
Correct Answer: (b) 14/11
Question from UPSC Prelims 2020 CSAT Paper
Explanation :
Recurring Decimal 1.272727…
To solve this problem, let x = 1.272727…
Then, 100x = 127.272727…
Subtracting x from 100x, we get:
- 99x = 126
- x = 126/99
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 3:
x = (126/3)/(99/3) = 42/33
We can simplify this fraction further by dividing the numerator and denominator by their greatest common factor, which is 3:
x = (42/3)/(33/3) = 14/11
Therefore, the recurring decimal representation 1.272727… is equivalent to 14/11, and the correct answer is (b).
