8/11 as a repeating decimal

Answer 1

To convert the fraction \( \frac{8}{11} \) into a decimal, you can perform long division or recognize that it is a repeating decimal.

Using long division:

1. Divide 8 by 11.
2. 11 goes into 80 (as we're focusing on decimal) 7 times (since \( 11 \times 7 = 77 \)).
3. Subtract 77 from 80, which gives you 3.
4. Bring down a 0 to get 30.
5. 11 goes into 30 twice (since \( 11 \times 2 = 22 \)).
6. Subtract 22 from 30, which gives you 8.
7. Bring down a 0 to get 80 again.

You will notice that the process will repeat from here, giving 7 and 2 again.

Hence, the decimal representation of \( \frac{8}{11} \) is:

\[ 0.\overline{72} \]

This means \( \frac{8}{11} \) as a repeating decimal is \( 0.727272...\) with "72" repeating indefinitely.