Question

Solve each problem using dimensional analysis. evey number must have a unit. work must be shown.
How many seconds are there in 2.5 years

Answer 1

To convert 2.5 years into seconds, we need to use dimensional analysis, which involves converting years to days, then days to hours, then hours to minutes, and finally minutes to seconds. Here are the steps:

1. **Convert years to days**:
- We know that there are approximately 365.25 days in a year (taking into account leap years).

\[
2.5 \, \text{years} \times \frac{365.25 \, \text{days}}{1 \, \text{year}} = 913.125 \, \text{days}
\]

2. **Convert days to hours**:
- There are 24 hours in a day.

\[
913.125 \, \text{days} \times \frac{24 \, \text{hours}}{1 \, \text{day}} = 21,915 \, \text{hours}
\]

3. **Convert hours to minutes**:
- There are 60 minutes in an hour.

\[
21,915 \, \text{hours} \times \frac{60 \, \text{minutes}}{1 \, \text{hour}} = 1,314,900 \, \text{minutes}
\]

4. **Convert minutes to seconds**:
- There are 60 seconds in a minute.

\[
1,314,900 \, \text{minutes} \times \frac{60 \, \text{seconds}}{1 \, \text{minute}} = 78,894,000 \, \text{seconds}
\]

5. **Final answer**:
\[
2.5 \, \text{years} = 78,894,000 \, \text{seconds}
\]

Thus, there are **78,894,000 seconds** in 2.5 years.