To convert the mixed number \( 2 \frac{7}{16} \) into a decimal using long division, we first need to convert the mixed number into an improper fraction.
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Convert \( 2 \frac{7}{16} \) to an improper fraction: \[ 2 \frac{7}{16} = \frac{2 \times 16 + 7}{16} = \frac{32 + 7}{16} = \frac{39}{16} \]
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Now, we will perform the long division of \( 39 \div 16 \).
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16 goes into 39 two times (because \( 16 \times 2 = 32 \)).
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Subtract \( 32 \) from \( 39 \): \[ 39 - 32 = 7 \]
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Now, bring down a zero (making it 70) because we want to convert it to a decimal.
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16 goes into 70 four times (because \( 16 \times 4 = 64 \)).
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Subtract \( 64 \) from \( 70 \): \[ 70 - 64 = 6 \]
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Bring down another zero (making it 60).
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16 goes into 60 three times (because \( 16 \times 3 = 48 \)).
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Subtract \( 48 \) from \( 60 \): \[ 60 - 48 = 12 \]
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Bring down another zero (making it 120).
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16 goes into 120 seven times (because \( 16 \times 7 = 112 \)).
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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 five times (because \( 16 \times 5 = 80 \)).
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Subtract \( 80 \) from \( 80 \): \[ 80 - 80 = 0 \]
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So, we have performed the division:
\[ 39 \div 16 = 2.4375 \]
Therefore, the decimal representation of \( 2 \frac{7}{16} \) is \( 2.4375 \).
The correct answer is: 2.4375