Question

Use long division to convert 2 and 7/16 to a decimal a 2.716 b 2.2857 c 0.4375 d 2.4375

Answer 1

To convert the mixed number \(2 \frac{7}{16}\) to a decimal, we'll first convert the fraction \(\frac{7}{16}\) to a decimal using long division.

**Step 1: Divide 7 by 16 using long division.**

1. 16 does not go into 7, so we look at 70 (adding a decimal and a zero).
2. 16 goes into 70 four times (since \(16 \times 4 = 64\)).
3. Subtract 64 from 70, which gives us a remainder of 6.
4. Bring down another 0, making it 60.
5. 16 goes into 60 three times (since \(16 \times 3 = 48\)).
6. Subtract 48 from 60, which gives us a remainder of 12.
7. Bring down another 0, making it 120.
8. 16 goes into 120 seven times (since \(16 \times 7 = 112\)).
9. Subtract 112 from 120, which gives us a remainder of 8.
10. Bring down another 0, making it 80.
11. 16 goes into 80 five times (since \(16 \times 5 = 80\)).
12. Subtract 80 from 80, which gives us a remainder of 0.

So, \(\frac{7}{16} = 0.4375\).

**Step 2: Add the whole number part back to the decimal of the fraction.**

The mixed number \(2 \frac{7}{16}\) can now be converted to a decimal:
\[
2 \frac{7}{16} = 2 + 0.4375 = 2.4375
\]

Thus, the decimal representation of \(2 \frac{7}{16}\) is \(2.4375\).

**The correct answer is (d) 2.4375.**