To convert the mixed number \( 6 \frac{7}{15} \) to a decimal, we first convert it to an improper fraction and then divide.
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Convert the mixed number to an improper fraction: \[ 6 \frac{7}{15} = \frac{6 \times 15 + 7}{15} = \frac{90 + 7}{15} = \frac{97}{15} \]
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Now we divide \( 97 \) by \( 15 \) using long division.
- Long Division Steps:
- \( 15 \) goes into \( 97 \) 6 times (because \( 15 \times 6 = 90 \)).
- Subtract \( 90 \) from \( 97 \) to get a remainder of \( 7 \).
- Bring down a \( 0 \) to make \( 70 \).
- \( 15 \) goes into \( 70 \) 4 times (because \( 15 \times 4 = 60 \)).
- Subtract \( 60 \) from \( 70 \) to get a remainder of \( 10 \).
- Bring down another \( 0 \) to make \( 100 \).
- \( 15 \) goes into \( 100 \) 6 times (because \( 15 \times 6 = 90 \)).
- Subtract \( 90 \) from \( 100 \) to get a remainder of \( 10 \).
- Bring down another \( 0 \) to make \( 100 \) again.
This shows that the division will repeat because we keep getting the same remainders. Therefore,
\[ 97 \div 15 = 6.46666... \]
This is approximately \( 6.47 \).
So, the correct answer to convert \( 6 \frac{7}{15} \) into decimal form is: ≈6.47.