Question

Use long dividon to convert 2 7/16 to a decimal
0.4375
2.4375
2.2857
2.716

Answer 1

To convert the mixed number \( 2 \frac{7}{16} \) into a decimal using long division, we first need to convert the mixed number into 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, we will perform the long division of \( 39 \div 16 \).

- 16 goes into 39 two times (because \( 16 \times 2 = 32 \)).
- Subtract \( 32 \) from \( 39 \):
\[
39 - 32 = 7
\]

- Now, bring down a zero (making it 70) because we want to convert it to a decimal.
- 16 goes into 70 four times (because \( 16 \times 4 = 64 \)).
- Subtract \( 64 \) from \( 70 \):
\[
70 - 64 = 6
\]

- Bring down another zero (making it 60).
- 16 goes into 60 three times (because \( 16 \times 3 = 48 \)).
- Subtract \( 48 \) from \( 60 \):
\[
60 - 48 = 12
\]

- Bring down another zero (making it 120).
- 16 goes into 120 seven times (because \( 16 \times 7 = 112 \)).
- Subtract \( 112 \) from \( 120 \):
\[
120 - 112 = 8
\]

- Bring down another zero (making it 80).
- 16 goes into 80 five times (because \( 16 \times 5 = 80 \)).
- Subtract \( 80 \) from \( 80 \):
\[
80 - 80 = 0
\]

So, we have performed the division:

\[
39 \div 16 = 2.4375
\]

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

The correct answer is:
**2.4375**