To convert the fraction \( \frac{10}{11} \) into a decimal, you can perform the division:
\( 10 \div 11 \).
When you do the division:
- 11 goes into 10 zero times, so you start with 0.
- Add a decimal point and a zero (making it 10.0), then divide again.
- 11 goes into 100 (after moving the decimal) nine times, since \( 11 \times 9 = 99 \).
- Subtract 99 from 100, which leaves 1.
- Bring down another 0, making it 10.
- Repeat the process: 11 goes into 10 zero times again, and again, you will have to bring down zeros.
Continuing this process results in:
\[ \frac{10}{11} = 0.909090\ldots \]
This is a repeating decimal. You can represent it as:
\[ 0.\overline{90} \]
Thus, the decimal representation of \( \frac{10}{11} \) is approximately \( 0.909 \) (with the "90" repeating).