To convert the mixed number \( 3 \frac{3}{8} \) to a decimal, we start by converting it entirely to an improper fraction.
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The mixed number can be converted to the improper fraction: \[ 3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8} \]
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Now we need to divide 27 by 8 to get the decimal representation:
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Set up the long division.
\[ 27 \div 8 \]
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8 goes into 27 three times (since \( 8 \times 3 = 24 \)). Place 3 above the division bar.
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Subtract 24 from 27, which leaves a remainder of 3.
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Now, bring down a zero (making it 30).
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8 goes into 30 three times (since \( 8 \times 3 = 24 \)). Place another 3 above the division bar, next to the previous 3.
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Subtract 24 from 30, leaving a remainder of 6.
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Bring down another zero (making it 60).
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8 goes into 60 seven times (since \( 8 \times 7 = 56 \)). Place 7 above the division bar.
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Subtract 56 from 60, leaving a remainder of 4.
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Bring down another zero (making it 40).
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8 goes into 40 five times (since \( 8 \times 5 = 40 \)). Place 5 above the division bar.
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Subtract 40 from 40, leaving a remainder of 0.
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Thus, the result of the long division is: \[ 3.375 \]
The decimal equivalent of \( 3 \frac{3}{8} \) is \( 3.375 \).
So, the correct answer is 3.375.