Question

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

0.4375
0.4375

2.716
2.716

2.2857
2.2857

2.4375

Answer 1

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

1. Convert \(2 \frac{7}{16}\) to an improper fraction:
\[
2 \frac{7}{16} = \frac{2 \times 16 + 7}{16} = \frac{32 + 7}{16} = \frac{39}{16}
\]

2. Now, divide \(39\) by \(16\) using long division.

- \(16\) goes into \(39\) two times.
- \(16 \times 2 = 32\)
- Subtract \(32\) from \(39\) to get \(7\).
- Bring down a zero (making it \(70\)).
- \(16\) goes into \(70\) four times.
- \(16 \times 4 = 64\)
- Subtract \(64\) from \(70\) to get \(6\).
- Bring down another zero (making it \(60\)).
- \(16\) goes into \(60\) three times.
- \(16 \times 3 = 48\)
- Subtract \(48\) from \(60\) to get \(12\).
- Bring down another zero (making it \(120\)).
- \(16\) goes into \(120\) seven times.
- \(16 \times 7 = 112\)
- Subtract \(112\) from \(120\) to get \(8\).
- Bring down another zero (making it \(80\)).
- \(16\) goes into \(80\) five times.
- \(16 \times 5 = 80\)
- Subtract \(80\) from \(80\) to get \(0\).

So, we have:
\[
39 \div 16 = 2.4375
\]

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