Question

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

≈0.46
approximately equals 0.46

6.715
6.715

≈6.47
approximately equals 6.47

≈6.14285

Answer 1

To convert \(6 \frac{7}{15}\) to a decimal using long division, we first convert the mixed number into an improper fraction.

1. Convert the mixed number \(6 \frac{7}{15}\) into an improper fraction:
\[
6 \frac{7}{15} = \frac{6 \times 15 + 7}{15} = \frac{90 + 7}{15} = \frac{97}{15}
\]

2. Now we perform the long division of \(97\) by \(15\).

- \(15\) goes into \(97\) a total of \(6\) times since \(15 \times 6 = 90\).
- Subtract \(90\) from \(97\):
\[
97 - 90 = 7
\]
- Now, place a decimal point and add a zero to get \(70\).
- \(15\) goes into \(70\) a total of \(4\) times since \(15 \times 4 = 60\).
- Subtract \(60\) from \(70\):
\[
70 - 60 = 10
\]
- Bring down another \(0\) to get \(100\).
- \(15\) goes into \(100\) a total of \(6\) times since \(15 \times 6 = 90\).
- Subtract \(90\) from \(100\):
\[
100 - 90 = 10
\]
- Bring down another \(0\) to get \(100\) again, and repeat the process.
- Continuing this, we realize that we will continue to get \(6\) for the next iterations.

Thus, the decimal representation for \(6 \frac{7}{15}\) is \(6.46666...\) which can be rounded to \(6.47.\)

So, the correct response is:
**≈6.47** approximately equals 6.47.