Question

Use long division to convert 6 7/15
6
7
15
to a decimal.(1 point)
Responses

6.715
6.715

≈0.46
≈
0.46
approximately equals 0.46

≈6.47
≈
6.47
approximately equals 6.47

≈6.14285

Answer 1

To convert the mixed number \( 6 \frac{7}{15} \) into a decimal using long division, follow these steps:

1. **Convert the mixed number to an improper fraction**.
\[
6 \frac{7}{15} = \frac{6 \times 15 + 7}{15} = \frac{90 + 7}{15} = \frac{97}{15}
\]

2. **Perform long division** of 97 by 15.

- 15 goes into 97 a total of 6 times (since \( 15 \times 6 = 90 \)).
- Subtract \( 90 \) from \( 97 \) which leaves a remainder of \( 7 \).

\[
97 - 90 = 7
\]

3. **Continue the division**:
- Now, we add a decimal point and a zero to the remainder, making it \( 70 \).
- 15 goes into 70 a total of 4 times (since \( 15 \times 4 = 60 \)).
- Subtract \( 60 \) from \( 70 \) which leaves a remainder of \( 10 \).

\[
70 - 60 = 10
\]

4. **Continue again**:
- Add another zero, making it \( 100 \).
- 15 goes into 100 a total of 6 times (since \( 15 \times 6 = 90 \)).
- Subtract \( 90 \) from \( 100 \) which leaves a remainder of \( 10 \).

\[
100 - 90 = 10
\]

5. This remainder of \( 10 \) will continue to produce results of \( 6 \) when we bring down another zero (it will result in \( 100 \) again). Therefore, the cycle starts repeating.

Thus, the decimal representation of \( 6 \frac{7}{15} \):
\[
6.46666...\text{ (repeats)}
\]
is approximately \( 6.47 \) when rounded to two decimal places.

The correct response from the options given is:
\[
\approx 6.47
\]