To convert \(2 \frac{7}{16}\) to a decimal using long division, follow these steps:
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Convert the mixed number 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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Perform the long division: Divide \(39\) by \(16\).
- \(16\) goes into \(39\) \(2\) times (since \(16 \times 2 = 32\)).
- Subtract \(32\) from \(39\): \(39 - 32 = 7\).
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Continue with the decimal:
- Add a decimal point to \(39\) and a zero to make it \(70\).
- \(16\) goes into \(70\) \(4\) times (since \(16 \times 4 = 64\)).
- Subtract \(64\) from \(70\): \(70 - 64 = 6\).
- Add another zero to make it \(60\).
- \(16\) goes into \(60\) \(3\) times (since \(16 \times 3 = 48\)).
- Subtract \(48\) from \(60\): \(60 - 48 = 12\).
- Add another zero to make it \(120\).
- \(16\) goes into \(120\) \(7\) times (since \(16 \times 7 = 112\)).
- Subtract \(112\) from \(120\): \(120 - 112 = 8\).
- Add another zero to make it \(80\).
- \(16\) goes into \(80\) \(5\) times (since \(16 \times 5 = 80\)).
- Subtract \(80\) from \(80\): \(80 - 80 = 0\).
Now, we put all the parts together: The result of dividing \(39\) by \(16\) gives us: \[ 2.4375 \]
So, the conversion of \(2 \frac{7}{16}\) to decimal is \(2.4375\).
The correct response is: 2.4375
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