The Number System Unit Test
Math 8 Q1 (Pre-Algebra) / The Number System
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 811 as a repeating decimal, we divide 811 by 9 since the repeating decimal will have a cycle of 9 digits.
811 ÷ 9 = 90 remainder 1
We see that the quotient is 90 and the remainder is 1. To express the repeating decimal, we write 90 as the whole number part and place a decimal point after it.
The repeating decimal will have a cycle of 9 digits, so we write the remainder 1 as the first digit after the decimal point, and place a bar over it to mark the cycle:
811 ÷ 9 = 90.111111111...
Therefore, 811 as a repeating decimal is 90.1 with the digit 1 repeating.
To express 811 as a repeating decimal, we need to divide 811 by a power of 10. Let's perform the division:
811 ÷ 10 = 81 with a remainder of 1
The remainder is 1. To continue the division, we add a zero after the remainder:
10 ÷ 10 = 1 with a remainder of 0
Now, let's continue the division:
100 ÷ 10 = 10 with a remainder of 0
And further:
1000 ÷ 10 = 100 with a remainder of 0
We can observe that the remainder is always 0 after each division. This indicates that the decimal representation of 811 doesn't repeat. Therefore, 811 as a decimal does not have a repeating decimal form.