The recurring decimal representation 1.272727... is equivalent to which one of the following?

Correct Answer: (B) 14/11

Let $x = 1.272727...$. Multiplying by 100 gives $100x = 127.272727...$. Subtracting the first equation from the second yields $99x = 126$, so $x =$$\frac{126}{99}$. Dividing both numerator and denominator by their greatest common divisor 9 gives $x =$$\frac{14}{11}$.