6. Juan found that his playlist will play for 7.6 * 10 ^ 2 seconds, 12. overline 6 * 10 ^ 5 * minutes 2. overline 10 * 10 ^ 4 * bours or 8. overline 79628 * 10 ^ 2 * days . Which answer uses the most appropriate units?
The answer that uses the most appropriate units is 8. overline 79628 * 10 ^ 2 * days.
To determine the most appropriate units for the given duration, we need to convert each option to a common unit and compare.
1. 7.6 * 10^2 seconds: This option is already in seconds.
2. 12. overline 6 * 10^5 * minutes: We need to convert minutes to seconds.
12. overline 6 * 10^5 * minutes = 12.6 * 10^5 * 60 seconds = 7.56 * 10^7 seconds.
3. 2. overline 10 * 10^4 * hours: We need to convert hours to seconds.
2. overline 10 * 10^4 * hours = 2.1 * 10^4 * 3600 seconds = 7.56 * 10^7 seconds.
4. 8. overline 79628 * 10^2 * days: We need to convert days to seconds.
8. overline 79628 * 10^2 * days = 8.79628 * 10^4 * 86400 seconds = 7.6 * 10^7 seconds.
Comparing the values, options 2, 3, and 4 all give us approximately 7.6 * 10^7 seconds. Therefore, any of these options can be considered as using the most appropriate units.
To determine which answer uses the most appropriate units, we need to compare the three options given: seconds, minutes, and days.
Let's examine each option one by one:
1. 7.6 * 10^2 seconds
2. 12.∅6 * 10^5 minutes
3. 8.∅79628 * 10^2 days
We can start by converting each option to the same base unit, such as seconds.
1. To convert seconds to seconds, we don't need to do anything. The unit remains the same.
2. To convert minutes to seconds, we know that there are 60 seconds in one minute. So, we can multiply the given value (12.∅6 * 10^5) by 60 to get the equivalent in seconds.
- (12.∅6 * 10^5) * 60 = (12.∅6 * 10^5) * (6 * 10^1) = (12.∅6 * 6) * (10^5 * 10^1) = 75.∅6 * 10^6
Thus, the value in seconds is 75.∅6 * 10^6 seconds.
3. To convert days to seconds, we know that there are 24 hours in one day and 60 minutes in one hour, resulting in 24 * 60 = 1440 minutes in one day. Moreover, there are 60 seconds in one minute.
So, we can multiply the given value (8.∅79628 * 10^2) by 1440 (to convert days to minutes) and then by 60 (to convert minutes to seconds).
- (8.∅79628 * 10^2) * 1440 * 60 = (8.∅79628 * 10^2) * (1.44 * 10^3) * (60) = (8.∅79628 * 1.44 * 60) * (10^2 * 10^3) = 8,799,897.6 * 10^6
Thus, the value in seconds is 8,799,897.6 * 10^6 seconds.
Now, comparing the values we found:
1. 7.6 * 10^2 seconds
2. 75.∅6 * 10^6 seconds
3. 8,799,897.6 * 10^6 seconds
Based on the comparisons, option 3, which expresses the time in seconds, provides the most appropriate units for the given playlist duration.