To convert the mixed number \( 5 \frac{3}{16} \) to a decimal using long division, follow these steps:
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First, convert the mixed number to an improper fraction: \[ 5 \frac{3}{16} = \frac{(5 \times 16) + 3}{16} = \frac{80 + 3}{16} = \frac{83}{16} \]
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Now, perform long division by dividing 83 by 16.
- 16 goes into 83:
- \( 16 \times 5 = 80 \) (Since \( 16 \times 6 = 96 \) which is too high)
- Write \( 5 \) above the division line.
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Subtract \( 80 \) from \( 83 \): \[ 83 - 80 = 3 \]
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Now, bring down a zero (since we want to convert to a decimal, we can add a decimal point and add a zero).
- Now we have \( 30 \).
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16 goes into 30:
- \( 16 \times 1 = 16 \)
- Write \( 1 \) next to \( 5 \) above the division line.
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Subtract \( 16 \) from \( 30 \): \[ 30 - 16 = 14 \]
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Bring down another zero (making it \( 140 \)).
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16 goes into 140:
- \( 16 \times 8 = 128 \)
- Write \( 8 \) next to \( 51 \).
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Subtract \( 128 \) from \( 140 \): \[ 140 - 128 = 12 \]
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Bring down another zero (making it \( 120 \)).
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16 goes into 120:
- \( 16 \times 7 = 112 \)
- Write \( 7 \) next to the previous results.
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Subtract \( 112 \) from \( 120 \): \[ 120 - 112 = 8 \]
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Bring down another zero (making it \( 80 \)).
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16 goes into 80:
- \( 16 \times 5 = 80 \)
- Write \( 5 \) next to the previous results.
- Subtract \( 80 \) from \( 80 \) to get \( 0 \).
The result of the division gives us: \[ 83 \div 16 = 5.1875 \]
Thus, \( 5 \frac{3}{16} \) as a decimal is \( \textbf{5.1875} \).
The answer is: 5.1875.
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