To express the fraction \( \frac{8}{11} \) as a repeating decimal, we divide 8 by 11.
- \( 11 \) goes into \( 80 \) (when we consider \( 8.0 \)) a total of \( 7 \) times, since \( 11 \times 7 = 77 \).
- Subtract \( 77 \) from \( 80 \), yielding \( 3 \).
- Bring down another \( 0 \), making it \( 30 \).
- \( 11 \) goes into \( 30 \) a total of \( 2 \) times, since \( 11 \times 2 = 22 \).
- Subtract \( 22 \) from \( 30 \), yielding \( 8 \).
- Bring down another \( 0 \) to make it \( 80 \) again.
Now we can see that we are repeating the steps.
Thus, \( \frac{8}{11} = 0.727272...\)
We can denote the repeating part with a bar:
\[ \frac{8}{11} = 0.\overline{72} \]
So, the final answer is:
\[ 0.\overline{72} \]