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...