To convert the mixed number \(3 \frac{3}{8}\) to a decimal, we can break it down into its components and convert the fractional part \( \frac{3}{8} \) using long division.
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First, convert the mixed number into an improper fraction: \[ 3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8} \]
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Now, perform long division to divide \(27\) by \(8\):
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\(8\) goes into \(27\) three times since \(8 \times 3 = 24\).
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Subtract \(24\) from \(27\) to find the remainder: \[ 27 - 24 = 3 \]
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Now, you have \(3\) left. To convert this into a decimal, you can add a decimal point and a zero (making it \(30\)):
- \(8\) goes into \(30\) three times since \(8 \times 3 = 24\).
- Subtract \(24\) from \(30\) to find the new remainder: \[ 30 - 24 = 6 \]
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Now, bring down another \(0\), making it \(60\):
- \(8\) goes into \(60\) seven times since \(8 \times 7 = 56\).
- Subtract \(56\) from \(60\) to find the new remainder: \[ 60 - 56 = 4 \]
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Bring down another \(0\), making it \(40\):
- \(8\) goes into \(40\) five times since \(8 \times 5 = 40\).
- Subtract \(40\) from \(40\) to find the new remainder: \[ 40 - 40 = 0 \]
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Since there is no remainder, the decimal representation of \( \frac{27}{8} \) is: \[ 3.375 \]
Thus, \(3 \frac{3}{8}\) as a decimal is:
3.375
The correct response is 3.375.