Question

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

≈6.47
approximately equals 6.47

≈6.14285
approximately equals 6.14285

6.715
6.715

≈0.46

Answer 1

To convert the mixed number \( 6 \frac{7}{15} \) to a decimal using long division, follow these steps:

1. **Separate the Whole Number and the Fraction**:
The mixed number \( 6 \frac{7}{15} \) can be expressed as \( 6 + \frac{7}{15} \).

2. **Convert the Fraction to Decimal**:
- We need to divide 7 by 15.
- Set up the long division for \( 7 \div 15 \).

Here's how it works:

- 15 goes into 70 (since 7.0 is the same as 70 tenths) four times (4), because \( 15 \times 4 = 60 \).
- Subtract \( 60 \) from \( 70 \), which leaves \( 10 \).
- Now bring down a zero, making it \( 100 \).
- 15 goes into 100 six times (6), because \( 15 \times 6 = 90 \).
- Subtract \( 90 \) from \( 100 \), which leaves \( 10 \) again.
- Bring down another zero, making it \( 100 \) again.
- This will repeat the previous steps.

Therefore, \( 7 \div 15 = 0.46666\ldots \) (which is \( 0.4\overline{6} \))

3. **Add the Whole Number**:
Now, add the whole number part:

\[
6 + 0.46666\ldots = 6.46666\ldots
\]

So, to two decimal places, the value rounds to **6.47**.

The answer options have the following values:
- **≈6.47 (approximately equals 6.47)**

Thus, the correct response is:
**≈6.47**