Question

Use long division to convert 3 3/8 to a decimal.(1 point)
Responses

33.75
33.75

0.375
0.375

2.66
2.66

3.375

Answer 1

To convert the mixed number \( 3 \frac{3}{8} \) to a decimal, we start by converting it entirely to an improper fraction.

1. The mixed number can be converted to the improper fraction:
\[
3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8}
\]

2. Now we need to divide 27 by 8 to get the decimal representation:
- Set up the long division.

\[
27 \div 8
\]

- 8 goes into 27 three times (since \( 8 \times 3 = 24 \)). Place 3 above the division bar.
- Subtract 24 from 27, which leaves a remainder of 3.

- Now, bring down a zero (making it 30).
- 8 goes into 30 three times (since \( 8 \times 3 = 24 \)). Place another 3 above the division bar, next to the previous 3.
- Subtract 24 from 30, leaving a remainder of 6.

- Bring down another zero (making it 60).
- 8 goes into 60 seven times (since \( 8 \times 7 = 56 \)). Place 7 above the division bar.
- Subtract 56 from 60, leaving a remainder of 4.

- Bring down another zero (making it 40).
- 8 goes into 40 five times (since \( 8 \times 5 = 40 \)). Place 5 above the division bar.
- Subtract 40 from 40, leaving a remainder of 0.

3. Thus, the result of the long division is:
\[
3.375
\]

The decimal equivalent of \( 3 \frac{3}{8} \) is \( 3.375 \).

So, the correct answer is **3.375**.