Use long division to convert 6 7/15

Question

to a decimal.(1 point)
Responses

≈0.46
approximately equals 0.46

6.715
6.715

≈6.14285
approximately equals 6.14285

≈6.47

Answer 1

To convert the mixed number \( 6 \frac{7}{15} \) to a decimal, you can first convert the fraction \( \frac{7}{15} \) to a decimal using long division. Here are the steps:

1. Set Up Long Division: Divide 7 by 15.

2. Determine How Many Times 15 Goes Into 7: 15 goes 0 times into 7, so write 0 and a decimal point.

3. Bring Down the Zero: Since we are dividing, we can keep the division going by adding a decimal and a 0. Now we are dividing 70 by 15.

4. Divide 70 by 15: 15 goes into 70 four times (because \( 15 \times 4 = 60 \)).

5. Subtract: \( 70 - 60 = 10 \).

6. Bring Down Another 0: We now have 100.

7. Divide 100 by 15: 15 goes into 100 six times (because \( 15 \times 6 = 90 \)).

8. Subtract: \( 100 - 90 = 10 \).

9. Bring Down Another 0: Now we have 100 again.

10. Repeat: The division will repeat, so we get 0.46666...

Now, the decimal representation of \( \frac{7}{15} \) is approximately \( 0.4667 \) (rounded to four decimal places).

Now we convert the mixed number:

• \( 6 \frac{7}{15} = 6 + 0.4667 \)

Adding these two together:

• \( 6 + 0.4667 \approx 6.4667 \)

The closest response from your options is:

≈6.47