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
3.375

Answer 1

To convert the mixed number \( 3 \frac{3}{8} \) to a decimal using long division, we'll first convert the mixed number to an improper fraction.

1. **Convert the mixed number to an improper fraction**:
- The whole number part is 3.
- The fraction part is \( \frac{3}{8} \).
- To convert it, we multiply the whole number (3) by the denominator (8) and add the numerator (3):
\[
3 \cdot 8 + 3 = 24 + 3 = 27.
\]
- So, we have:
\[
3 \frac{3}{8} = \frac{27}{8}.
\]

2. **Now we perform long division to find \( \frac{27}{8} \)**:
- 27 divided by 8.
- 8 goes into 27 three times, since \( 8 \times 3 = 24 \).
- Subtract 24 from 27, which leaves a remainder of 3.
- We can write this as:
\[
27 \div 8 = 3 \quad \text{remainder } 3.
\]
- Now we add a decimal place and a zero (turning 3 into 30).
- Now divide 30 by 8, which goes 3 times (since \( 8 \times 3 = 24 \)).
- Subtract again: \( 30 - 24 = 6 \).
- Bring down another zero, making it 60.
- Now divide 60 by 8, which goes 7 times (since \( 8 \times 7 = 56 \)).
- Subtract: \( 60 - 56 = 4 \).
- Bring down another zero, making it 40.
- Now divide 40 by 8, which goes 5 times (since \( 8 \times 5 = 40 \)).
- Subtract: \( 40 - 40 = 0 \).

Putting it all together, we have:
- The whole number is 3,
- The first decimal part is 3,
- The second decimal part is 7,
- The third decimal part is 5.

So, \( 3 \frac{3}{8} = 3.375 \).

Therefore, the decimal equivalent of \( 3 \frac{3}{8} \) is **3.375**.

**Answer: 3.375**