To convert \( \frac{3}{16} \) to a decimal using long division, follow these steps:
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Set up the division by placing 3 under the long division symbol and 16 outside.
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Since 3 is less than 16, we add a decimal point and a zero to 3, making it 30. We also need to add another zero to continue the division.
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Divide 30 by 16. The closest multiple of 16 that fits into 30 is 16 (which is \( 16 \times 1 = 16 \)).
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Write 1 above the division line and subtract 16 from 30: \[ 30 - 16 = 14 \]
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Bring down the next zero (making it 140).
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Divide 140 by 16. The closest multiple of 16 is 128 (which is \( 16 \times 8 = 128 \)).
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Write 8 above the division line and subtract 128 from 140: \[ 140 - 128 = 12 \]
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Bring down the next zero (making it 120).
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Divide 120 by 16. The closest multiple of 16 is 112 (which is \( 16 \times 7 = 112 \)).
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Write 7 above the division line and subtract 112 from 120: \[ 120 - 112 = 8 \]
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Bring down the next zero (making it 80).
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Divide 80 by 16. The closest multiple of 16 is 64 (which is \( 16 \times 5 = 80 \)).
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Write 5 above the division line and subtract 80 from 80: \[ 80 - 80 = 0 \]
Since we have a remainder of 0, we can stop here.
Putting it all together, the decimal representation of \( \frac{3}{16} \) is:
\[ 0.1875 \]
Thus, \( \frac{3}{16} = 0.1875 \).