Question

preston told his best friend that someone sailed around the world alone in $3.6 \times 10^{6}$ seconds. what would be the most appropriate unit of time for preston to use instead of seconds?\
minutes\
hours\
days\
years

Explanation:

Step1: Recall time conversions

We know that \(1\) minute \( = 60\) seconds, \(1\) hour \( = 60\) minutes \(= 60\times60 = 3600\) seconds, \(1\) day \( = 24\) hours \(=24\times3600=86400\) seconds, and \(1\) year \(\approx365\times86400 = 31536000\) seconds.

Step2: Convert \(3.6\times 10^{6}\) seconds to other units

• To minutes: \(\frac{3.6\times 10^{6}}{60}=6\times 10^{4}\) minutes (60000 minutes), which is a large number.
• To hours: \(\frac{3.6\times 10^{6}}{3600}=1000\) hours.
• To days: \(\frac{3.6\times 10^{6}}{86400}\approx41.67\) days.
• To years: \(\frac{3.6\times 10^{6}}{31536000}\approx0.114\) years.

Among these, days give a value around 40 which is a reasonable number to represent the time taken to sail around the world alone (a few weeks to a couple of months is a typical range, and 40 days is within that). Minutes and hours give very large or less intuitive numbers, and years give a fraction which is not as intuitive as days for this context.

Answer:

days