The recurring decimal representation 1.272727 is equivalent to

The recurring decimal representation 1.272727 … is equivalent to

1. 13/11
2. 14/11
3. 127/99
4. 137/99

• Answer: The correct option is B
• Explanation:

  Method I:

  1.272727… can be written as 1 + 0.272727…

  = 1 + 3(0.909…) 

  = 1 + 3(1/11) {since, 0.909…. = 1/11} 

  = 1+ (3/11)

  = 14/11

  Method II:

  Let x = 1.272727…

  100x = 127.272727…

  So, 100x - x = (127.272727….) - (1.272727….)

  99x = 126

  x = 126/99

  = 14/11

• Exam Year: 2020