Question

Use long division to convert 7/11 to a decimal a squiggly lines 1.571428 B squiggly lines 0.63 C 63 d 7.11

Answer 1

To convert \( \frac{7}{11} \) to a decimal using long division, follow these steps:

1. **Set up the long division:** Divide 7 by 11.

2. **Initial Division:**
- 11 goes into 7, 0 times.
- Place a decimal point and add a zero, making it 70.

3. **Next Division:**
- 11 goes into 70, 6 times (since \( 11 \times 6 = 66 \)).
- Write down 6 after the decimal point.
- Subtract 66 from 70; you get 4.

4. **Bring down a zero:**
- Now you have 40.
- 11 goes into 40, 3 times (since \( 11 \times 3 = 33 \)).
- Write down 3.
- Subtract 33 from 40; you get 7.

5. **Bring down another zero:**
- Now you have 70 again.
- 11 goes into 70, 6 times.
- Subtract 66 from 70; you get 4.

6. **Continue the process:**
- Bring down a zero to make it 40.
- 11 goes into 40, 3 times.
- Subtract 33 from 40; you get 7.

You will notice that the process is repeating. The decimal continues as \( 0.636363 \ldots \), which we can represent as \( 0.63\overline{63} \).

Thus, the decimal representation of \( \frac{7}{11} \) is \( 0.636363...\).

Now, looking at the answer options:
- **A**: ~1.571428
- **B**: ~0.63 (using the notation for repeating decimals, we could write it as \( 0.63\overline{63} \))
- **C**: 63
- **D**: 7.11

The correct choice is **B** (0.63 with squiggly lines indicating the repeating part).