# 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).