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 999, which is the largest three-digit decimal number.
811 ÷ 999 = 0.811811811...
So, 811 can be expressed as the repeating decimal 0.811 with the cycle of repeating digits marked with a bar above them.
To express 811 as a repeating decimal, we can divide 811 by the denominator of its fraction, which is 999.
Here are the steps to do the long division:
0.811
___________
999 | 811.000
We start by dividing 8 by 9, which equals 0 with a remainder of 8. Write down the quotient, 0, and bring down the next digit, 1, to create 81.
0.811
___________
999 | 811.000
-0
Next, we divide 81 by 9, which equals 9 with a remainder of 0. Write down the quotient, 9, and bring down the next digit, 1, to create 10.
0.811
___________
999 | 811.000
-0
9
______
10
Finally, we divide 10 by 9, which equals 1 with a remainder of 1. Write down the quotient, 1, and bring down the next digit, 0, to create 10.
0.811
___________
999 | 811.000
-0
9
______
10
-9
______
100
Since we now have a remainder of 10, we continue dividing until we get a repeating decimal.
We divide 10 by 9, which equals 1 with a remainder of 1. Write down the quotient, 1, and bring down another 0 to create 10.
0.811
___________
999 | 811.000
-0
9
______
10
-9
______
100
- 99
________
10
We divide 10 by 9 once again, which equals 1 with a remainder of 1. Write down the quotient, 1, and bring down another 0 to create 10.
0.811
___________
999 | 811.000
-0
9
______
10
-9
______
100
- 99
________
10
- 9
_______
10
As we can see, the remainder stays as 10, and the decimal digits 1 and 0 repeat indefinitely after the decimal point.
Therefore, the decimal representation of 811 as a repeating decimal is 0.811̅, with the bar placed over the digits 1 and 0.