Question

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

6.715
6.715

≈6.14285
approximately equals 6.14285

≈0.46
approximately equals 0.46

≈6.47

Answer 1

To convert the mixed number \(6 \frac{7}{15}\) to a decimal, we can break it down into its components:

1. The whole number part is 6.
2. We need to convert the fractional part \(\frac{7}{15}\) into a decimal.

To do this, we can use long division to divide 7 by 15.

**Long Division:**

1. 15 goes into 7: 0 times (since 7 is less than 15).
2. We can write this as \(0.\) (so far we have \(0.0\)).
3. We add a decimal point and a zero to the 7, making it 70.
4. 15 goes into 70: 4 times (since \(15 \times 4 = 60\)).
5. Subtract \(60\) from \(70\), which gives us \(10\).
6. Bring down another zero, making it \(100\).
7. 15 goes into 100: 6 times (since \(15 \times 6 = 90\)).
8. Subtract \(90\) from \(100\), which gives us \(10\).
9. Bring down another zero, making it \(100\).
10. Repeat steps 7-9, and you’ll find that the cycle repeats every two divisions.

Putting this together, we find that:

\[
\frac{7}{15} \approx 0.4666\ldots \text{ (with 6 repeating)}
\]

Now, we can add this decimal to the whole number:

\[
6 + 0.4666\ldots = 6.4666\ldots
\]

Rounding to two decimal places gives us approximately \(6.47\).

Thus, the final answer for the conversion of \(6 \frac{7}{15}\) to a decimal is:

**≈ 6.47**