Express 8/11 as repeating decimal
To express 8/11 as a repeating decimal, you can use long division. Follow these steps:
1. Divide 8 by 11: 8 ÷ 11 = 0.72
2. Since the decimal division is not yet complete, put a decimal point after the 2 in 0.72.
3. Multiply the remainder (8) by 10 to get the next digit: 8 x 10 = 80.
4. Divide 80 by 11: 80 ÷ 11 = 7 with a remainder of 3.
5. Bring down a zero and repeat the process: add a decimal point after the 7, multiply the remainder (3) by 10, and divide by 11: 30 ÷ 11 = 2 with a remainder of 8.
6. Repeat the process until the desired level of accuracy is reached.
Continue this process of multiplying and dividing until you either reach the desired level of accuracy or notice a recurring pattern. In this case, we see that the remainder becomes 8 again, so the decimal representation of 8/11 is 0.72(72), where the 72 repeats infinitely.
Therefore, 8/11 as a repeating decimal is 0.72(72).