Question

4/11 as a repeating decimal...

Answer 1

To convert the fraction \( \frac{4}{11} \) into a repeating decimal, we can perform the long division of 4 by 11.

1. **Set up the division**: 4.000000... divided by 11.
2. \( 11 \) goes into \( 40 \) three times since \( 11 \times 3 = 33 \).
- Subtract \( 33 \) from \( 40 \) to get \( 7 \).
3. Bring down the next zero, making it \( 70 \).
- \( 11 \) goes into \( 70 \) six times since \( 11 \times 6 = 66 \).
- Subtract \( 66 \) from \( 70 \) to get \( 4 \).
4. Bring down another zero, making it \( 40 \) again.
- Repeat the steps: \( 11 \) goes into \( 40 \) three times, leaving \( 7 \).
5. It will continue this way, alternating between \( 3 \) and \( 6 \).

Thus, the decimal representation of \( \frac{4}{11} \) is:

\[
0.\overline{36}
\]

This indicates that the digits \( 36 \) repeat indefinitely.