Answer:
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.
