Question

Use long division to convert 3 and 4/5 to a decimal

Answer 1

To convert the mixed number \( 3 \frac{4}{5} \) to a decimal using long division, we can follow these steps:

1. **Convert the mixed number to an improper fraction**:
\[
3 \frac{4}{5} = \frac{(3 \times 5) + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5}
\]

2. **Divide the numerator by the denominator using long division**:
We need to divide \( 19 \) by \( 5 \).

- **Step 1**: How many times does \( 5 \) fit into \( 19 \)? It fits \( 3 \) times because \( 5 \times 3 = 15 \).
- **Step 2**: Subtract \( 15 \) from \( 19 \):
\[
19 - 15 = 4
\]
- **Step 3**: Since there is a remainder, we can add a decimal point and a zero, making it \( 40 \).
- **Step 4**: Divide \( 40 \) by \( 5 \). \( 5 \) goes into \( 40 \) exactly \( 8 \) times because \( 5 \times 8 = 40 \).
- **Step 5**: Subtract \( 40 \) from \( 40 \):
\[
40 - 40 = 0
\]

Since there is no remainder, the division process stops here.

3. **Combine the results**:
The result of the long division gives us:
\[
19 \div 5 = 3.8
\]
Therefore, the decimal representation of \( 3 \frac{4}{5} \) is \( 3.8 \).

So, \( 3 \frac{4}{5} = 3.8 \).