Question

Use long division to convert 4/15 to a decimal.(1 point)
Responses

4.15
4.15

3.75
3.75

≈0.27
approximately equals 0.27

26
26

Answer 1

To convert \( \frac{4}{15} \) to a decimal using long division, follow these steps:

1. **Set up the long division**: Divide 4 (the numerator) by 15 (the denominator). Since 4 is less than 15, you start with 0.
2. **Add decimal places**: Add a decimal point and zeros to the dividend (4.000...).
3. **Divide**:
- How many times does 15 go into 40? It goes 2 times (because \( 15 \times 2 = 30 \)).
- Write 2 above the line.
- Subtract \( 30 \) from \( 40 \) to get \( 10 \).
4. **Bring down the next zero**: Bringing down another zero makes it \( 100 \).
5. **Repeat the process**:
- How many times does 15 go into \( 100 \)? It goes 6 times (because \( 15 \times 6 = 90 \)).
- Write 6 above the line next to 2.
- Subtract \( 90 \) from \( 100 \) to get \( 10 \).
6. **Bring down another zero**, and you again have \( 100 \).
7. **Repeat the division**: You'll again get 6, and this process will repeat indefinitely.

Thus, the decimal is:
\[ 0.2666...\]
or approximately:
\[ 0.27\]

So the correct answer is:
**≈0.27**.