janiya found that her playlist will play for 3.8*10^2 seconds, 6.3̅ *10^5 minutes, 1.05̅ *10^4 hours, or 4.3̅9̅8̅1̅4̅ * 10^2 days. which answer uses the most appropriate units?
3.8*10^7 seconds
6.3̅ *10^5 minutes
1.05̅ *10^4 hours
4.3̅9̅8̅1̅4̅ * 10^2 days
To determine which answer uses the most appropriate units, we need to compare the different units provided: seconds, minutes, hours, and days.
First, let's convert all the given units to a common unit. Since seconds is the base unit of time, it makes sense to convert all the units to seconds for easier comparison.
To convert minutes to seconds, we multiply by 60 (since there are 60 seconds in 1 minute):
6.3̅ * 10^5 minutes = 6.3̅ * 10^5 * 60 seconds = 3.78 * 10^7 seconds
To convert hours to seconds, we multiply by 60 minutes (since there are 60 minutes in 1 hour) and then by 60 seconds:
1.05̅ * 10^4 hours = 1.05̅ * 10^4 * 60 * 60 seconds = 3.78 * 10^7 seconds
To convert days to seconds, we multiply by 24 hours (since there are 24 hours in 1 day), then by 60 minutes, and finally by 60 seconds:
4.3̅9̅8̅1̅4̅ * 10^2 days = 4.3̅9̅8̅1̅4̅ * 10^2 * 24 * 60 * 60 seconds = 3.73 * 10^7 seconds
Comparing the converted values, we can see that all the options have approximately the same magnitude, around 3.8 * 10^7 seconds. However, the most appropriate unit is the one that provides a whole number without any repeating digits or approximation.
The most appropriate unit is 3.8 * 10^7 seconds.