To convert the mixed number \(2 \frac{7}{16}\) to a decimal using long division, follow these steps:
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Separate the whole number and the fraction:
- The whole number is \(2\).
- The fraction is \(\frac{7}{16}\).
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Convert the fraction to a decimal:
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Perform long division of \(7\) by \(16\).
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Long Division:
- \(16\) into \(70\) goes \(4\) times (since \(16 \times 4 = 64\)).
- Subtract \(64\) from \(70\) to get \(6\).
- Bring down a zero, making it \(60\).
- \(16\) into \(60\) goes \(3\) times (since \(16 \times 3 = 48\)).
- Subtract \(48\) from \(60\) to get \(12\).
- Bring down another zero, making it \(120\).
- \(16\) into \(120\) goes \(7\) times (since \(16 \times 7 = 112\)).
- Subtract \(112\) from \(120\) to get \(8\).
- Bring down another zero, making it \(80\).
- \(16\) into \(80\) goes \(5\) times (since \(16 \times 5 = 80\)).
- Subtract \(80\) from \(80\) to get \(0\).
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The result of the long division is \(0.4375\).
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Combine the whole number and the decimal:
- Add the whole number \(2\) to the decimal \(0.4375\): \[ 2 + 0.4375 = 2.4375 \]
Thus, the decimal representation of \(2 \frac{7}{16}\) is 2.4375.
The correct response is: 2.4375.
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