Question

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

Answer 1

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.

Answer 2

30/11

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.