Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
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To express 811 as a repeating decimal, we can divide 811 by 999 (which is one less than 1000, so it will have a repeating decimal pattern of 3 digits).
$$\begin{array}{c|c}
811 & 999 \\
- 799 & \\
\hline
12 & \\
- 9 & \\
\hline
30 & \\
\end{array}$$
We can see that the remainder repeats after the first division, so the decimal representation of 811 is 0.812812812... The cycle of repeating digits is 812.
To express 811 as a repeating decimal, we need to divide 811 by 1,000. This will give us the decimal representation of the number.
811 ÷ 1,000 = 0.811
However, since we want the repeating decimal representation, we need to multiply the result by a power of 10. In this case, we will multiply by 10 to the power of 3, which is 1,000.
0.811 × 1,000 = 811
So, the repeating decimal representation of 811 is 0.811.