Janiya found that her playlist will play for 3.8×1^02 seconds, 6.3¯¯¯ ×10^5minutes, 1.05¯¯¯¯¯ ×10^4 hours, or 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×10^2 days. Which answer uses the most appropriate units?(1 point)

1.05 ¯¯¯¯¯¯ ×10^4 hours

3.8×10^7 seconds

6.3¯¯¯ ×10^5 minutes

4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×10^2 days

1 answer

To determine which answer uses the most appropriate units, let's convert the different time measurements to a common unit (for example, days) for comparison.

  1. Seconds to Days: \[ \text{Seconds in a day} = 60 \text{ seconds/minute} \times 60 \text{ minutes/hour} \times 24 \text{ hours/day} = 86400 \text{ seconds/day} \] \[ 3.8 \times 10^7 \text{ seconds} = \frac{3.8 \times 10^7}{86400} \approx 439.5 \text{ days} \]

  2. Minutes to Days: \[ \text{Minutes in a day} = 60 \text{ minutes/hour} \times 24 \text{ hours/day} = 1440 \text{ minutes/day} \] \[ 6.3 \times 10^5 \text{ minutes} = \frac{6.3 \times 10^5}{1440} \approx 437.5 \text{ days} \]

  3. Hours to Days: \[ 1.05 \times 10^4 \text{ hours} = \frac{1.05 \times 10^4}{24} \approx 437.5 \text{ days} \]

  4. Days: \[ 4.39814 \times 10^2 \text{ days} = 439.814 \text{ days} \]

Now let's summarize the results:

  • 3.8 × 10^7 seconds ≈ 439.5 days
  • 6.3 × 10^5 minutes ≈ 437.5 days
  • 1.05 × 10^4 hours ≈ 437.5 days
  • 4.39814 × 10^2 days = 439.814 days

The answer that uses the most appropriate units, which is the most easily understood and is measured in days, is: 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×10^2 days