To convert \( \frac{7}{11} \) to a decimal using long division, we divide 7 by 11.
- Since 7 is less than 11, we start with 0. We will put the decimal point and add a zero (making it 70).
- Now, we divide 70 by 11:
- 11 goes into 70 a total of 6 times (because \( 11 \times 6 = 66 \)).
- Write 6 after the decimal point. The result so far is 0.6.
- Subtract \( 66 \) from \( 70 \), which gives \( 4 \). Bring down another 0, making it \( 40 \).
- Now, divide 40 by 11:
- 11 goes into 40 a total of 3 times (because \( 11 \times 3 = 33 \)).
- Write 3 after the 6. The result so far is 0.63.
- Subtract \( 33 \) from \( 40 \), leaving \( 7 \). Bring down another 0, making it \( 70 \) again, and repeat the process.
- 70 divided by 11 gives you the earlier result of 6, followed by a zero (making it \( 0.63636... \)).
The long division will keep cycling between 6 and 3 indefinitely.
Thus, the decimal representation of \( \frac{7}{11} \) is approximately \( 0.6363...\), which can also be written in a rounded form as \( 0.636 \) or approximately \( 0.6364 \).
Among the options provided, the closest answer is \( \approx 0.63 \).