To convert the mixed number \( 6 \frac{7}{15} \) to a decimal using long division, follow these steps:
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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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Perform long division of 97 by 15:
- 15 goes into 97 a total of 6 times (because \( 15 \times 6 = 90 \)).
- Subtract 90 from 97 to get a remainder of 7.
- Bring down a 0 to make it 70. Now divide 70 by 15.
- 15 goes into 70 a total of 4 times (because \( 15 \times 4 = 60 \)).
- Subtract 60 from 70 to get a remainder of 10.
- Bring down another 0 to make it 100. Now divide 100 by 15.
- 15 goes into 100 a total of 6 times (because \( 15 \times 6 = 90 \)).
- Subtract 90 from 100 to get a remainder of 10 again.
- Bring down another 0 to make it 100 again.
This gives us:
- \( 6.4...\)
Continuing this process:
- 15 goes into 100 a total of 6 times again, followed by a repeating remainder.
Continuing this would show that the decimal \( 6.46666... \) repeats with the 6.
- Final Result: Thus, \( 6 \frac{7}{15} \) as a decimal is approximately \( 6.47 \) when rounded.
So, the exact response to the options is: \(\approx 6.47\).
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