To solve this problem, we need to convert each time period into a fraction of a year. To simplify our calculations, let's assume a year consists of 365 days (not considering leap years).
1. Convert days to fractions of a year:
- 190 days:
[tex]\[
\frac{190}{365} \approx 0.5205
\][/tex]
- 160 days:
[tex]\[
\frac{160}{365} \approx 0.4384
\][/tex]
- 200 days:
[tex]\[
\frac{200}{365} \approx 0.5479
\][/tex]
2. Convert months to fractions of a year: (Assuming each month has 30 days)
- 5 months:
5 months = 5 × 30 = 150 days
[tex]\[
\frac{150}{365} \approx 0.4110
\][/tex]
- 7 months:
7 months = 7 × 30 = 210 days
[tex]\[
\frac{210}{365} \approx 0.5753
\][/tex]
Now, we have all the fractions:
- 190 days ≈ 0.5205
- 5 months ≈ 0.4110
- 160 days ≈ 0.4384
- 7 months ≈ 0.5753
- 200 days ≈ 0.5479
3. Arrange these fractions in ascending order:
- First, 5 months: [tex]\( \approx 0.4110 \)[/tex]
- Second, 160 days: [tex]\( \approx 0.4384 \)[/tex]
- Third, 190 days: [tex]\( \approx 0.5205 \)[/tex]
- Fourth, 200 days: [tex]\( \approx 0.5479 \)[/tex]
- Fifth, 7 months: [tex]\( \approx 0.5753 \)[/tex]
Therefore, the fractions of the year in ascending order are:
[tex]\[
0.4110, 0.4384, 0.5205, 0.5479, 0.5753
\][/tex]
