Janiya found that her playlist will play for 3.8×102 seconds, 6.3¯¯¯ ×10^5 minutes, 1.05¯¯¯¯¯ ×10^4 hours, or 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×10^2 days. Which answer uses the most appropriate units?(1 point)
Responses
6.3¯¯¯ ×105 minutes
6 point modifying above 3 with bar times 10 superscript 5 baseline minutes
4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×102 days
4 point modifying above 39814 with bar times 10 squared days
3.8×107 seconds
3.8 times 10 superscript 7 baseline seconds
1.05 ¯¯¯¯¯¯ ×104 hours
1.05¯ × 10^4 hours
The answer that uses the most appropriate units is 3.8 × 10^7 seconds.
To determine which answer uses the most appropriate units, we need to convert all the units to the same base unit. In this case, we can convert everything to either seconds, minutes, hours, or days.
Let's start by examining the options:
1. 6.3¯¯¯ × 10^5 minutes: To convert this to seconds, we multiply by 60 since there are 60 seconds in a minute. Therefore, 6.3¯¯¯ × 10^5 minutes is equal to (6.3¯¯¯ × 10^5) * 60 = 3.78¯¯¯ × 10^7 seconds.
2. 4.39814¯¯¯¯¯¯¯¯ × 10^2 days: To convert this to seconds, we multiply by 24 (hours in a day), then by 60 (minutes in an hour), and finally by 60 again (seconds in a minute). Therefore, 4.39814¯¯¯¯¯¯¯¯ × 10^2 days is equal to (4.39814¯¯¯¯¯¯¯¯ × 10^2) * 24 * 60 * 60 = 3.79984672 × 10^7 seconds.
3. 3.8×10^7 seconds: This is already in seconds, so no conversion is necessary.
4. 1.05¯¯¯¯¯ × 10^4 hours: To convert this to seconds, we multiply by 60 (minutes in an hour) and then by 60 again (seconds in a minute). Therefore, 1.05¯¯¯¯¯ × 10^4 hours is equal to (1.05¯¯¯¯¯ × 10^4) * 60 * 60 = 3.78¯¯¯ × 10^7 seconds.
Based on the conversions, options 1 and 4 give us the same value in seconds as option 3. However, option 2 gives us a slightly higher value. Therefore, the answer that uses the most appropriate units is:
2. 4.39814¯¯¯¯¯¯¯¯ × 10^2 days
This answer is in terms of days, which provides a larger unit of time and is more appropriate for the given duration.