To convert the mixed number \( 3 \frac{4}{5} \) to a decimal using long division, follow these steps:
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Convert the mixed number to an improper fraction: \[ 3 \frac{4}{5} = \frac{(3 \times 5) + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} \]
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Set up long division to divide 19 by 5:
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5 goes into 19 three times (because \( 5 \times 3 = 15 \)).
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Write down 3, then subtract 15 from 19, which gives you a remainder of: \[ 19 - 15 = 4 \]
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Now bring down a 0 (making it 40).
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Now, see how many times 5 goes into 40. It goes 8 times (because \( 5 \times 8 = 40 \)).
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Write down 8, then subtract 40 from 40, which gives you a remainder of: \[ 40 - 40 = 0 \]
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Putting it together:
You have obtained the result of the division: \[ 19 \div 5 = 3.8 \]
Therefore, the decimal equivalent of \( 3 \frac{4}{5} \) is \( 3.8 \).