Question

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

2.2857


2.4375


2.716


0.4375

Answer 1

To convert the mixed number \(2 \frac{7}{16}\) to a decimal using long division, we first need to convert it to an improper fraction.

1. Convert the mixed number \(2 \frac{7}{16}\):
- Multiply the whole number (2) by the denominator (16): \(2 \times 16 = 32\).
- Add the numerator (7): \(32 + 7 = 39\).
- So, \(2 \frac{7}{16} = \frac{39}{16}\).

2. Now, perform long division of 39 by 16.

- 16 goes into 39 two times (since \(2 \times 16 = 32\)).
- Subtract \(32\) from \(39\) to get \(7\).
- Bring down a zero to make it \(70\).

3. Now, divide \(70\) by \(16\):
- 16 goes into 70 four times (since \(4 \times 16 = 64\)).
- Subtract \(64\) from \(70\) to get \(6\).
- Bring down another zero to make it \(60\).

4. Divide \(60\) by \(16\):
- 16 goes into 60 three times (since \(3 \times 16 = 48\)).
- Subtract \(48\) from \(60\) to get \(12\).
- Bring down another zero to make it \(120\).

5. Divide \(120\) by \(16\):
- 16 goes into 120 seven times (since \(7 \times 16 = 112\)).
- Subtract \(112\) from \(120\) to get \(8\).
- Bring down another zero to make it \(80\).

6. Divide \(80\) by \(16\):
- 16 goes into 80 five times (since \(5 \times 16 = 80\)).
- Subtract \(80\) from \(80\) to get \(0\).

Putting it all together, the result of the long division is:

\[
2.4375
\]

So, \(2 \frac{7}{16} = 2.4375\).

Therefore, the correct response is:

**2.4375**