To convert the fraction \( \frac{7}{11} \) into a decimal, we can perform the division:
- Divide 7 by 11.
Starting with \( 7.000000 \):
- \( 11 \) goes into \( 70 \) six times (since \( 11 \times 6 = 66 \)).
- Subtract \( 66 \) from \( 70 \) to get \( 4 \).
- Bring down the next \( 0 \) to get \( 40 \).
- \( 11 \) goes into \( 40 \) three times (since \( 11 \times 3 = 33 \)).
- Subtract \( 33 \) from \( 40 \) to get \( 7 \).
- Bring down the next \( 0 \) to get \( 70 \), and we are back to where we started.
This process shows that the decimal will continue to repeat. Therefore, we have:
\[ \frac{7}{11} = 0.636363\ldots \]
We can denote this repeating decimal by using a bar over the repeating digits:
\[ \frac{7}{11} = 0.\overline{63} \]
Thus, the final answer is:
\[ \frac{7}{11} = 0.\overline{63} \]