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 \( 0.0647 \).