The recurring decimal representation 1.272727... is equivalent to
Answer & explanation
Answer: (b) 14/11
The repeating block 27 has two digits, so 0·2727... = 27/99 = 3/11. Adding the whole part gives 1 + 3/11 = 14/11.
- Let x = 1·2727...; then 100x = 127·2727...
- 100x − x = 126, so x = 126/99 = 14/11.
- Check: 14 ÷ 11 = 1·2727...
Remember · A pure recurring decimal 0·(ab) repeating = ab/99; handle the whole-number part separately.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·