Solve each problem using dimensional analysis. evey number must have a unit. work must be shown.

Question

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:
\[ \boxed{1.62 , \text{weeks}} \]