Question

Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)

Answer 1

To convert the fraction \( \frac{8}{11} \) into a decimal, we can perform long division.

1. Divide 8 by 11.
- 11 goes into 80 seven times (since \( 11 \times 7 = 77 \)).
- Subtract \( 77 \) from \( 80 \) to get \( 3 \).
- Bring down a \( 0 \) to make it \( 30 \).

2. Divide 30 by 11.
- 11 goes into 30 two times (since \( 11 \times 2 = 22 \)).
- Subtract \( 22 \) from \( 30 \) to get \( 8 \).
- Bring down another \( 0 \) to make it \( 80 \) again.

At this point, we notice the repeat since we are back to dividing 80 by 11, the same as in step 1.

Putting it all together, we have:

- The whole number part: 0
- The decimal part begins after the point: \( 72 \)

Thus, we find:

\[
\frac{8}{11} = 0.72\overline{72}
\]

So, expressed as a repeating decimal, \( \frac{8}{11} \) is \( 0.\overline{72} \).