Janiya found that her playlist will play for 3.8 x 10^2 seconds, 6.3 x 10^5 minutes, 1.05 x 10^4 hours, or 4.39814 x 10^2 days. Which answer uses the most appropriate units?
a 3.8 x 10^7 seconds
b 4.39814 x 10^2 days
c 6.3 x 10^5 minutes
d 1.05 x 10^4 hours
The most appropriate units for the length of Janiya's playlist would be days. Therefore, the answer is:
b) 4.39814 x 10^2 days
To determine the most appropriate units, we need to convert all the given values to the same unit of time.
We can convert the given values as follows:
3.8 x 10^2 seconds = 3.8 x 10^2 seconds
6.3 x 10^5 minutes = 6.3 x 10^5 minutes = 6.3 x 10^5 minutes x 60 seconds/minute = 3.78 x 10^7 seconds
1.05 x 10^4 hours = 1.05 x 10^4 hours = 1.05 x 10^4 hours x 60 minutes/hour = 6.3 x 10^5 minutes
Comparing the converted values, we can see that option c) 6.3 x 10^5 minutes uses the most appropriate units.
To determine the most appropriate units, we need to convert all the given units to the same base unit. Let's convert them all to seconds for comparison:
a) 3.8 x 10^2 seconds
b) 4.39814 x 10^2 days -> 4.39814 x 10^2 * 24 (hours in a day) * 60 (minutes in an hour) * 60 (seconds in a minute)
c) 6.3 x 10^5 minutes -> 6.3 x 10^5 * 60 (seconds in a minute)
d) 1.05 x 10^4 hours -> 1.05 x 10^4 * 60 (minutes in an hour) * 60 (seconds in a minute)
Calculating these conversions:
a) 3.8 x 10^2 seconds = 380 seconds
b) 4.39814 x 10^2 * 24 * 60 * 60 = 38016 seconds
c) 6.3 x 10^5 * 60 = 37800000 seconds
d) 1.05 x 10^4 * 60 * 60 = 37800000 seconds
Comparing the converted values, we can see that answer b) 4.39814 x 10^2 days represents the highest value in seconds. So the most appropriate unit is b) 4.39814 x 10^2 days.