Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point) $$

Question

GPT-4o mini · Answer

To express $ \frac{8}{11} $ as a repeating decimal, we can perform the long division of 8 by 11. 1. Divide 8 by 11. Since 8 is less than 11, we place a decimal point and add a zero. This allows us to divide 80 by 11. 2. $ 11 $ goes into $ 80 $ a total of $ 7 $ times (since $ 11 \times 7 = 77 $). 3. Subtract $ 77 $ from $ 80 $ to get $ 3 $. 4. Bring down another $ 0 $, making it $ 30 $. 5. $ 11 $ goes into $ 30 $ $ 2 $ times (since $ 11 \times 2 = 22 $). 6. Subtract $ 22 $ from $ 30 $ to get $ 8 $. 7. Bring down another $ 0 $, making it $ 80 $ again. 8. At this point, we see that we have returned to $ 80 $, which means the sequence will repeat. Thus, the decimal representation of $ \frac{8}{11} $ is: $$ 0.\overline{72} $$ The repeating decimal is $ 0.\overline{72} $, with the digits $ 72 $ repeating indefinitely.