Question

Use long division to convert 2 7/16
to a decimal.(1 point)
Responses

2.2857
2.2857

2.716
2.716

2.4375
2.4375

0.4375
0.4375

Answer 1

To convert the mixed number \(2 \frac{7}{16}\) to a decimal using long division, follow these steps:

1. **Separate the whole number and the fraction**:
- The whole number is \(2\).
- The fraction is \(\frac{7}{16}\).

2. **Convert the fraction to a decimal**:
- Perform long division of \(7\) by \(16\).

- **Long Division**:
- \(16\) into \(70\) goes \(4\) times (since \(16 \times 4 = 64\)).
- Subtract \(64\) from \(70\) to get \(6\).
- Bring down a zero, making it \(60\).
- \(16\) into \(60\) goes \(3\) times (since \(16 \times 3 = 48\)).
- Subtract \(48\) from \(60\) to get \(12\).
- Bring down another zero, making it \(120\).
- \(16\) into \(120\) goes \(7\) times (since \(16 \times 7 = 112\)).
- Subtract \(112\) from \(120\) to get \(8\).
- Bring down another zero, making it \(80\).
- \(16\) into \(80\) goes \(5\) times (since \(16 \times 5 = 80\)).
- Subtract \(80\) from \(80\) to get \(0\).

- The result of the long division is \(0.4375\).

3. **Combine the whole number and the decimal**:
- Add the whole number \(2\) to the decimal \(0.4375\):
\[
2 + 0.4375 = 2.4375
\]

Thus, the decimal representation of \(2 \frac{7}{16}\) is **2.4375**.

The correct response is:
**2.4375**.