Janiya found that her playlist will play for 3.8 x 10^2 seconds, 6.3 x 10^5minutes, 1.05 x 10^4hours, 4.39814 x 10^2 days. Which answer uses the most appropriate units?
1. 3.8 x 10^2 seconds
2. 6.3 x 10^5minutes
3. 1.05 x 10^4hours
4. 4.39814 x 10^2 days
4. 4.39814 x 10^2 days
The most appropriate answer in terms of units would be option 4. 4.39814 x 10^2 days.
To determine the most appropriate unit for Janiya's playlist, we need to consider the relative size of each unit and select the largest one.
Option 1: 3.8 x 10^2 seconds
Option 2: 6.3 x 10^5 minutes
Option 3: 1.05 x 10^4 hours
Option 4: 4.39814 x 10^2 days
To compare the units, we need to convert them to a common unit. The most commonly used unit for measuring large durations of time is days. Let's convert each option to days to determine which one is the largest.
Option 1: 3.8 x 10^2 seconds
To convert seconds to days, we divide by the number of seconds in a day (24 hours * 60 minutes * 60 seconds).
3.8 x 10^2 seconds ÷ (24 hours * 60 minutes * 60 seconds) = 0.00462962963 days
Option 2: 6.3 x 10^5 minutes
To convert minutes to days, we divide by the number of minutes in a day (24 hours * 60 minutes).
6.3 x 10^5 minutes ÷ (24 hours * 60 minutes) = 437.5 days
Option 3: 1.05 x 10^4 hours
To convert hours to days, we divide by the number of hours in a day (24 hours).
1.05 x 10^4 hours ÷ 24 hours = 437.5 days
Option 4: 4.39814 x 10^2 days
This option is already in days, so there's no need for conversion.
Comparing the results:
Option 1: 0.00462962963 days
Option 2: 437.5 days
Option 3: 437.5 days
Option 4: 4.39814 x 10^2 days
It is clear that Option 2: 6.3 x 10^5minutes gives the largest value in days. Therefore, Option 2 (6.3 x 10^5 minutes) uses the most appropriate units.