Question

se long division to convert 6 7/20
to a decimal.(1 point)
Responses

0.35
0.35

6.285714
6.285714

6.35
6.35

6.72

Answer 1

To convert \( 6 \frac{7}{20} \) to a decimal using long division, we can first convert the mixed number into an improper fraction.

1. Convert \( 6 \frac{7}{20} \) to an improper fraction:
\[
6 \frac{7}{20} = \frac{(6 \times 20) + 7}{20} = \frac{120 + 7}{20} = \frac{127}{20}
\]

2. Now, we will divide 127 by 20 using long division:

- 20 goes into 127 six times (since \( 20 \times 6 = 120 \)).
- Subtract 120 from 127 to find the remainder:
\[
127 - 120 = 7
\]
- Now, we have \( 6 \) as the whole number, and the remainder is \( 7 \). To continue with decimal places, we can add a decimal point and a zero (making it 70) to our dividend:

3. Divide 70 by 20:
- 20 goes into 70 three times (since \( 20 \times 3 = 60 \)).
- Subtract 60 from 70:
\[
70 - 60 = 10
\]
- Add another zero to get 100.

4. Divide 100 by 20:
- 20 goes into 100 five times (since \( 20 \times 5 = 100 \)).
- Subtract 100 from 100:
\[
100 - 100 = 0
\]

Putting this all together, we find:
\[
6 \frac{7}{20} = 6.35
\]

So, the final answer is **6.35**.