Question

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

Responses

≈6.47
approximately equals 6.47

≈0.46
approximately equals 0.46

≈6.14285
approximately equals 6.14285

6.715

Answer 1

To convert the mixed number \(6 \frac{7}{15}\) to a decimal, we'll first convert it into an improper fraction and then perform long division.

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. **Now perform long division of \(97\) by \(15\):**

- \( 15 \) goes into \( 97 \) a total of \( 6 \) times (because \( 15 \times 6 = 90 \)).
- Subtract \( 90 \) from \( 97 \), which gives \( 7 \).
- Bring down a \( 0 \) (considering it like \( 7.0 \)) making it \( 70 \).
- \( 15 \) goes into \( 70 \) a total of \( 4 \) times (because \( 15 \times 4 = 60 \)).
- Subtract \( 60 \) from \( 70 \), which gives \( 10 \).
- Bring down another \( 0 \) (making it \( 100 \)).
- \( 15 \) goes into \( 100 \) a total of \( 6 \) times (because \( 15 \times 6 = 90 \)).
- Subtract \( 90 \) from \( 100 \) giving \( 10 \).
- Bring down another \( 0 \) (making it \( 100 \)) and repeat.

Continuing this, you can see that the process will result in \( 6.46666...\), which can be rounded to:

\[
6.47
\]

So the answer is:

**≈6.47** approximately equals 6.47.