Question

Use long division to convert 6 7/15%0D%0A6%0D%0A7%0D%0A15%0D%0A to a decimal.(1 point)%0D%0AResponses%0D%0A%0D%0A≈0.46%0D%0A≈%0D%0A0.46%0D%0Aapproximately equals 0.46%0D%0A%0D%0A≈6.47%0D%0A≈%0D%0A6.47%0D%0Aapproximately equals 6.47%0D%0A%0D%0A≈6.14285%0D%0A≈%0D%0A6.14285%0D%0Aapproximately equals 6.14285%0D%0A%0D%0A6.715

Answer 1

To convert \( 6 \frac{7}{15} \% \) to a decimal, we first convert the mixed number to an improper fraction and then to a decimal.

1. **Convert the mixed number to an improper fraction**:
\[
6 \frac{7}{15} = \frac{6 \times 15 + 7}{15} = \frac{90 + 7}{15} = \frac{97}{15}
\]

2. **Convert the percentage to a decimal**:
To convert the fraction \( \frac{97}{15} \% \) to a decimal, we divide it by 100 (since 1% = 0.01):
\[
\frac{97}{15} \div 100 = \frac{97}{15} \times \frac{1}{100} = \frac{97}{1500}
\]

3. **Perform long division to convert \( \frac{97}{1500} \) to a decimal**:
We divide 97 by 1500.

- 1500 goes into 9700 (we multiply by 100 to eliminate the decimal) zero times, that's 0.
- Shifting our focus, we see how many times 1500 goes into 9700. 1500 goes into 9700 six times (since \( 1500 \times 6 = 9000 \)).
- Substracting gives \( 9700 - 9000 = 700 \). Bring down the next zero (which was added after the decimal), bringing us to 7000.
- 1500 goes into 7000 four times (since \( 1500 \times 4 = 6000 \)).
- Substracting gives \( 7000 - 6000 = 1000 \). Bring down the next zero to make it 10000.
- 1500 goes into 10000 six times (since \( 1500 \times 6 = 9000 \)).
- Substracting gives \( 10000 - 9000 = 1000 \). Bring down the next zero to get 10000.
- Continuing on, we would keep getting 6 (as shown before) forever, leading to the repeating decimal.

From our calculations:
\[
\frac{97}{1500} = 0.06467...
\]
Thus, to answer your question, \( 6 \frac{7}{15} \% \approx 0.06467 \).

This indicates the decimal equivalent of \( 6 \frac{7}{15} \% \) is approximately \( 0.06467 \).

**Final Answer:**
The decimal value of \( 6 \frac{7}{15} \% \) is approximately \( 0.0647 \).