Question

Solve each problem using dimensional analysis. evey number must have a unit. work must be shown.
How many weeks are in 16,300 minutes

Answer 1

To convert minutes to weeks using dimensional analysis, we need to know the following conversion factors:

1 hour = 60 minutes
1 day = 24 hours
1 week = 7 days

Now, we can set up the dimensional analysis.

1. Start with the known quantity:
\( 16,300 \, \text{minutes} \)

2. Convert minutes to hours:
\[
16,300 \, \text{minutes} \times \frac{1 \, \text{hour}}{60 \, \text{minutes}} = \frac{16,300}{60} \, \text{hours}
\]

Now calculating this:
\[
\frac{16,300}{60} \approx 271.67 \, \text{hours}
\]

3. Convert hours to days:
\[
271.67 \, \text{hours} \times \frac{1 \, \text{day}}{24 \, \text{hours}} = \frac{271.67}{24} \, \text{days}
\]

Now calculating this:
\[
\frac{271.67}{24} \approx 11.32 \, \text{days}
\]

4. Convert days to weeks:
\[
11.32 \, \text{days} \times \frac{1 \, \text{week}}{7 \, \text{days}} = \frac{11.32}{7} \, \text{weeks}
\]

Now calculating this:
\[
\frac{11.32}{7} \approx 1.62 \, \text{weeks}
\]

Thus, the final answer is:
\[
\boxed{1.62 \, \text{weeks}}
\]