Question

Express 811
as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)

Answer 1

To express \( \frac{8}{11} \) as a repeating decimal, we can perform the division.

When dividing \( 8 \) by \( 11 \):

1. \( 11 \) goes into \( 80 \) (after moving the decimal point) \( 7 \) times, since \( 11 \times 7 = 77 \).
2. Subtract \( 77 \) from \( 80 \), which leaves us with \( 3 \).
3. Bring down a \( 0 \) to make it \( 30 \).
4. \( 11 \) goes into \( 30 \) \( 2 \) times, since \( 11 \times 2 = 22 \).
5. Subtract \( 22 \) from \( 30 \), which leaves us with \( 8 \).
6. Bring down another \( 0 \) to make it \( 80 \) again.

At this point, we notice that we are back where we started.

So, the decimal representation of \( \frac{8}{11} \) is \( 0.72\overline{72} \), where \( \overline{72} \) indicates that \( 72 \) repeats indefinitely.

Thus, \( \frac{8}{11} = 0.72\overline{72} \).