Question
exspress 8/11 as a reapeating decimal. mark the cycleo repeatign digits witha bar
Answers
Answered by
GPT-4o mini
To express \( \frac{8}{11} \) as a repeating decimal, you can perform long division or recognize the pattern in the division.
When dividing 8 by 11:
1. \( 8 \div 11 = 0 \) (bring down a decimal and a zero)
2. \( 80 \div 11 = 7 \) (since 11 goes into 80 seven times, which makes 77)
3. The remainder is \( 80 - 77 = 3 \)
4. Bring down another 0 to make it 30.
5. \( 30 \div 11 = 2 \) (since 11 goes into 30 two times, which makes 22)
6. The remainder is \( 30 - 22 = 8 \)
7. Bring down another 0 to make it 80 again, which brings you back to the previous steps.
This process reveals a repeating cycle:
So, \( \frac{8}{11} = 0.72\overline{72} \).
Thus, as a repeating decimal, it can be expressed as \( 0.72\overline{72} \), where the bar indicates that "72" is the repeating part.
When dividing 8 by 11:
1. \( 8 \div 11 = 0 \) (bring down a decimal and a zero)
2. \( 80 \div 11 = 7 \) (since 11 goes into 80 seven times, which makes 77)
3. The remainder is \( 80 - 77 = 3 \)
4. Bring down another 0 to make it 30.
5. \( 30 \div 11 = 2 \) (since 11 goes into 30 two times, which makes 22)
6. The remainder is \( 30 - 22 = 8 \)
7. Bring down another 0 to make it 80 again, which brings you back to the previous steps.
This process reveals a repeating cycle:
So, \( \frac{8}{11} = 0.72\overline{72} \).
Thus, as a repeating decimal, it can be expressed as \( 0.72\overline{72} \), where the bar indicates that "72" is the repeating part.