To convert the mixed number \(3 \frac{3}{8}\) to a decimal using long division, follow these steps:
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First, convert the mixed number to 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, divide \(27\) by \(8\) using long division.
- \(8\) goes into \(27\) three times because \(8 \times 3 = 24\).
- Subtract \(24\) from \(27\): \[ 27 - 24 = 3 \]
- Bring down a zero to the remainder \(3\) to make it \(30\).
- \(8\) goes into \(30\) three times because \(8 \times 3 = 24\).
- Subtract \(24\) from \(30\): \[ 30 - 24 = 6 \]
- Bring down a zero to make it \(60\).
- \(8\) goes into \(60\) seven times because \(8 \times 7 = 56\).
- Subtract \(56\) from \(60\): \[ 60 - 56 = 4 \]
- Bring down a zero to make it \(40\).
- \(8\) goes into \(40\) five times because \(8 \times 5 = 40\).
- Subtract \(40\) from \(40\): \[ 40 - 40 = 0 \]
So, the result of the division gives: \[ 27 \div 8 = 3.375 \]
Thus, the decimal representation of \(3 \frac{3}{8}\) is \(3.375\).
Final Answer: 3.375