Question

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

2.66
2.66

3.375
3.375

0.375
0.375

33.75

Answer 1

To convert the mixed number \(3 \frac{3}{8}\) to a decimal, we can break it down into its components and convert the fractional part \( \frac{3}{8} \) using long division.

1. First, convert the mixed number into an improper fraction:
\[
3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8}
\]

2. Now, perform long division to divide \(27\) by \(8\):

- \(8\) goes into \(27\) three times since \(8 \times 3 = 24\).
- Subtract \(24\) from \(27\) to find the remainder:
\[
27 - 24 = 3
\]

- Now, you have \(3\) left. To convert this into a decimal, you can add a decimal point and a zero (making it \(30\)):
- \(8\) goes into \(30\) three times since \(8 \times 3 = 24\).
- Subtract \(24\) from \(30\) to find the new remainder:
\[
30 - 24 = 6
\]

- Now, bring down another \(0\), making it \(60\):
- \(8\) goes into \(60\) seven times since \(8 \times 7 = 56\).
- Subtract \(56\) from \(60\) to find the new remainder:
\[
60 - 56 = 4
\]

- Bring down another \(0\), making it \(40\):
- \(8\) goes into \(40\) five times since \(8 \times 5 = 40\).
- Subtract \(40\) from \(40\) to find the new remainder:
\[
40 - 40 = 0
\]

Since there is no remainder, the decimal representation of \( \frac{27}{8} \) is:
\[
3.375
\]

Thus, \(3 \frac{3}{8}\) as a decimal is:

**3.375**

The correct response is **3.375**.