Question

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

6.35
6.35

0.35
0.35

6.72
6.72

6.285714

Answer 1

To convert \( 6 \frac{7}{20} \) to a decimal using long division, we first need to convert the fractional part \( \frac{7}{20} \) to a decimal.

1. **Set up the long division**: We divide 7 by 20.

\[
20 \text{ goes into } 7: 0 \text{ times}
\]
So we can write \( 7.000 \) for the long division to help in our calculation.

2. **Add decimal point**: Place a decimal point in the quotient and in the dividend:
- 20 into 70 (since we shift the decimal and consider 7.0 as 70).

3. **Long division**:
- \( 20 \) goes into \( 70 \) three times because \( 20 \times 3 = 60 \).
- Subtract \( 60 \) from \( 70 \): \( 70 - 60 = 10 \).

4. **Bring down the next digit (which is 0, making it 100)**:
- Now, ask how many times \( 20 \) goes into \( 100 \).
- \( 20 \) goes into \( 100 \) five times because \( 20 \times 5 = 100 \).
- Subtract \( 100 \) from \( 100 \): \( 100 - 100 = 0 \).

Now we have completed the division, finding that:

\[
\frac{7}{20} = 0.35
\]

Next, we add this result to the whole number part \( 6 \):

\[
6 + 0.35 = 6.35
\]

Therefore, \( 6 \frac{7}{20} \) as a decimal is:

\[
\boxed{6.35}
\]