Express 811 as a repeating decima

To express 811 as a repeating decimal, we can first divide 811 by 1000:

811 ÷ 1000 = 0.811

Since 811 is a whole number, we can rewrite it as 811/1. Then, to convert the fraction 811/1 into a repeating decimal, we can multiply both the numerator and denominator by the same power of 10, which in this case is 1000:

(811/1) × (1000/1000) = 811000/1000 = 811

Now, we can express 811 as a repeating decimal by placing a horizontal line (vinculum) over the repeating part, which is 811:

811 = 0.811

Thus, 811 can be expressed as a repeating decimal as 0.811.

To express 811 as a repeating decimal, divide 811 by the number 9 since we want to find the fraction equivalent of the repeating decimal.

811 ÷ 9 = 90 with a remainder of 1

Write the quotient 90, then the decimal point at the top, and the remainder 1 as a numerator over the divisor 9 as the denominator.

811 ÷ 9 = 90.1

Now, since the remainder is not zero, we will have a repeating decimal.

To find the repeating part, we multiply the remainder by 10 and divide by the divisor, which is still 9 in this case.

1 × 10 = 10

10 ÷ 9 = 1 with a remainder of 1

We now repeat the previous step and multiply the remainder (1) by 10 and divide by 9.

1 × 10 = 10

10 ÷ 9 = 1 with a remainder of 1

Therefore, the repeating part is 1.

Putting it all together, the decimal representation of 811 as a repeating decimal is:

811/9 = 90.111...