To determine which number \(3 \frac{3}{7}\) is closest to when rounded to the nearest half, let's follow these steps:
1. Convert the Mixed Fraction to a Decimal:
A mixed fraction \(3 \frac{3}{7}\) can be converted to a decimal by treating it as the sum of its whole part and its fractional part:
[tex]\[
3 \frac{3}{7} = 3 + \frac{3}{7}
\][/tex]
Calculate \(\frac{3}{7}\):
[tex]\[
\frac{3}{7} \approx 0.42857142857142855
\][/tex]
Then add this to the whole number:
[tex]\[
3 + 0.42857142857142855 \approx 3.4285714285714284
\][/tex]
2. Compare with Possible Answers:
Next, we compare this decimal value \(3.4285714285714284\) against each of the given options:
- Option A: 3
[tex]\[
|3.4285714285714284 - 3| = 0.4285714285714284
\][/tex]
- Option B: \(3 \frac{1}{4}\)
[tex]\[
3 \frac{1}{4} = 3 + \frac{1}{4} = 3 + 0.25 = 3.25
\][/tex]
[tex]\[
|3.4285714285714284 - 3.25| = 0.17857142857142838
\][/tex]
- Option C: \(3 \frac{1}{2}\)
[tex]\[
3 \frac{1}{2} = 3 + 0.5 = 3.5
\][/tex]
[tex]\[
|3.4285714285714284 - 3.5| = 0.07142857142857162
\][/tex]
- Option D: 4
[tex]\[
|3.4285714285714284 - 4| = 0.5714285714285716
\][/tex]
3. Determine the Option with the Smallest Difference:
Now, we observe the absolute differences calculated:
- \( |3.4285714285714284 - 3| = 0.4285714285714284 \)
- \( |3.4285714285714284 - 3.25| = 0.17857142857142838 \)
- \( |3.4285714285714284 - 3.5| = 0.07142857142857162 \)
- \( |3.4285714285714284 - 4| = 0.5714285714285716 \)
The smallest difference is \(0.07142857142857162\), which corresponds to \(3 \frac{1}{2}\).
Therefore, the mixed fraction \(3 \frac{3}{7}\) rounded to the nearest half is:
Answer: \(3 \frac{1}{2}\):
Option C.) [tex]\(3 \frac{1}{2}\)[/tex]
