Question

Use long division to convert 7/11 to a decimal.(1 point)
Responses

≈1.571428
approximately equals 1.571428

63
63

≈0.63
approximately equals 0.63

7.11

Answer 1

To convert \( \frac{7}{11} \) to a decimal using long division, we divide 7 by 11.

1. **Set up the long division:**
- 11 goes into 7, 0 times. Write 0 and place a decimal point. We can add zeros to 7 to continue the division.
- So we have 0.7, which is 7.0.

2. **Now divide 70 by 11:**
- 11 goes into 70, 6 times (since \( 11 \times 6 = 66 \)).
- Write down 6 next to the decimal point, so we now have 0.6.

3. **Subtract 66 from 70:**
- \( 70 - 66 = 4 \).
- Bring down another 0 (making it 40).

4. **Now divide 40 by 11:**
- 11 goes into 40, 3 times (since \( 11 \times 3 = 33 \)).
- Write down 3, so we have 0.63.

5. **Subtract 33 from 40:**
- \( 40 - 33 = 7 \).
- Bring down another 0 (making it 70 again).

6. **Repeat the process:**
- 11 goes into 70, 6 times (again giving us 66).
- Subtract: \( 70 - 66 = 4 \). Bring down another 0 (40).
- 11 goes into 40, 3 times (again giving us 33).
- Subtract: \( 40 - 33 = 7 \). Bring down another 0 (70).

Through this process, we see that the decimal repeats. Thus, the decimal representation of \( \frac{7}{11} \) is:

\[ 0.636363... \]

This can also be denoted as \( 0.\overline{63} \).

Among the options you provided, the closest representation is:

≈0.63 (approximately equals 0.63).