The recurring decimal representation 1.272727… is equivalent to

Correct Option (B)

The given recurring decimal is 1.272727..., which can be written as 1.27, where the digits '27' repeat. To convert this into a fraction, follow these steps:

Let x = 1.272727... (Equation 1)

Since two digits are repeating, multiply Equation 1 by 100:

100x = 127.272727... (Equation 2)

Subtract Equation 1 from Equation 2:

100x - x = 127.272727... - 1.272727...

99x = 126

x = 126/99

To simplify the fraction, divide both the numerator and the denominator by their greatest common divisor, which is 9:

x = (126 ÷ 9) / (99 ÷ 9)

x = 14/11

Therefore, the recurring decimal 1.272727... is equivalent to 14/11.

Incorrect Options:

• Option (A) 13/11: Converting 13/11 to a decimal yields 1.181818..., which is 1.18 recurring. This does not match the given decimal 1.272727....
• Option (C) 127/99: Converting 127/99 to a decimal yields 1.282828..., which is 1.28 recurring. This does not match the given decimal 1.272727....
• Option (D) 137/99: Converting 137/99 to a decimal yields 1.383838..., which is 1.38 recurring. This does not match the given decimal 1.272727....