Question

Express 811
8
11
as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
$$

Answer 1

To convert the fraction \(\frac{811}{8}\) into a decimal, we first perform the division.

1. Divide 811 by 8:

- 8 goes into 81 ten times (8 × 10 = 80).
- Subtract 80 from 81, which gives 1.
- Bring down the next digit (1), making it 11.
- 8 goes into 11 once (8 × 1 = 8).
- Subtract 8 from 11, which gives 3.
- Bring down the next digit (0), making it 30.
- 8 goes into 30 three times (8 × 3 = 24).
- Subtract 24 from 30, which gives 6.
- Bring down the next 0, making it 60.
- 8 goes into 60 seven times (8 × 7 = 56).
- Subtract 56 from 60, which gives 4.
- Bring down the next 0, making it 40.
- 8 goes into 40 five times (8 × 5 = 40).
- Subtract 40 from 40, which gives 0.

So, after this division, we find that:

\[
\frac{811}{8} = 101.375
\]

Since the division has a finite remainder leading to a finite answer, it does not have a repeating part in this case. Thus, the decimal representation of \(\frac{811}{8}\) is:

\[
101.375
\]

Since the decimal is non-repeating, you do not need to mark a cycle, and the final answer is simply:

\[
101.375
\]