To convert \(6 \frac{7}{15}\) to a decimal using long division, we first convert the mixed number into an improper fraction.
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Convert the mixed number \(6 \frac{7}{15}\) into 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 perform the long division of \(97\) by \(15\).
- \(15\) goes into \(97\) a total of \(6\) times since \(15 \times 6 = 90\).
- Subtract \(90\) from \(97\): \[ 97 - 90 = 7 \]
- Now, place a decimal point and add a zero to get \(70\).
- \(15\) goes into \(70\) a total of \(4\) times since \(15 \times 4 = 60\).
- Subtract \(60\) from \(70\): \[ 70 - 60 = 10 \]
- Bring down another \(0\) to get \(100\).
- \(15\) goes into \(100\) a total of \(6\) times since \(15 \times 6 = 90\).
- Subtract \(90\) from \(100\): \[ 100 - 90 = 10 \]
- Bring down another \(0\) to get \(100\) again, and repeat the process.
- Continuing this, we realize that we will continue to get \(6\) for the next iterations.
Thus, the decimal representation for \(6 \frac{7}{15}\) is \(6.46666...\) which can be rounded to \(6.47.\)
So, the correct response is: ≈6.47 approximately equals 6.47.
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