To convert the mixed number \(3\frac{3}{8}\) to a decimal using long division, we will first convert the mixed number into an improper fraction:
\[ 3\frac{3}{8} = 3 + \frac{3}{8} = \frac{24}{8} + \frac{3}{8} = \frac{27}{8} \]
Now, we will divide \(27\) by \(8\) using long division.
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Set up the division: \(27\) is the dividend, and \(8\) is the divisor.
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Determine how many times \(8\) goes into \(27\).
- \(8\) goes into \(27\) (3 times): \[ 8 \times 3 = 24 \]
- Write \(3\) above the division line.
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Subtract \(24\) from \(27\): \[ 27 - 24 = 3 \]
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Now bring down a zero (since we're looking for a decimal) to make it \(30\).
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Determine how many times \(8\) goes into \(30\).
- \(8\) goes into \(30\) (3 times): \[ 8 \times 3 = 24 \]
- Write \(3\) after the decimal point above the division line.
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Subtract \(24\) from \(30\): \[ 30 - 24 = 6 \]
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Bring down another zero to make it \(60\).
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Determine how many times \(8\) goes into \(60\).
- \(8\) goes into \(60\) (7 times): \[ 8 \times 7 = 56 \]
- Write \(7\) next to the \(3\).
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Subtract \(56\) from \(60\): \[ 60 - 56 = 4 \]
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Bring down another zero to make it \(40\).
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Determine how many times \(8\) goes into \(40\).
- \(8\) goes into \(40\) (5 times): \[ 8 \times 5 = 40 \]
- Write \(5\) next to the \(37\).
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Subtract \(40\) from \(40\): \[ 40 - 40 = 0 \]
This means we’ve reached a remainder of \(0\). Therefore, the decimal representation of \(3\frac{3}{8}\) is:
\[ 3.375 \]
So, \(3\frac{3}{8} = 3.375\).
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