Write repeating decimal 2.72727272 ... as a fraction. Reduce the fraction completely.

30/11

Step-by-step explanation:

Let's say x = 2.7272727272 ... If we multiply both sides by 100, we get:

100x = 272.7272727272 ...

We now have the equations:

100x = 272.7272727272 ...

x = 2.7272727272 ...

Let's subtract the second from the first. Doing so results in 99x on the left. On the right, the entire repeating part (72727272 ...) cancels out and we're just left with 272 - 2 = 270:

99x = 270

Divide by 99 on both sides:

x = 270 / 99

Simplify:

x = 30 / 11

The answer is 30/11.