Express 8/11 as a repeating decimal mark the cycle of repeating digits with a bar
To express 8/11 as a repeating decimal, you can long divide 8 by 11.
0.
+ 72 CANNOT DIVIDE BY 11
- 66 DIVIDED BY 11 EQUALS 6
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60
- 55 DIVIDED BY 11 EQUALS 5
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50
- 44 DIVIDED BY 11 EQUALS 4
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60
- 55 DIVIDED BY 11 EQUALS 5
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Keep dividing and you will continue to get the same pattern of "6" and "4" after the decimal point.
So, 8/11 as a repeating decimal is 0.72727272...
To express 8/11 as a repeating decimal, we need to perform long division. Let's start:
0.727272...
First, we divide 8 by 11. The quotient is 0 and the remainder is 8.
0.727272...
________________
11 | 8.00000000000
- 0
________
8
Next, we bring down another 0, making the new dividend equal to 80.
0.727272...
________________
11 | 8.00000000000
- 0
________
80
We divide 80 by 11, resulting in a quotient of 7 and a remainder of 3.
0.727272...
________________
11 | 8.00000000000
- 0
________
80
-77
______
30
We bring down another 0 and divide the new dividend, which is 30, by 11. This gives a quotient of 2 and a remainder of 8.
0.727272...
________________
11 | 8.00000000000
- 0
________
80
-77
______
30
-22
____
80
We can see that the remainder 8 matches the original dividend 8, showing that the division cycle will repeat from this point onward.
So, the fraction 8/11 can be expressed as a repeating decimal as follows:
8/11 = 0.727272...
The repeating cycle of digits is 72, which is marked with a bar over the top: 0.72̅