How Can Dimensional Analysis Be Used to Determine the Number of Seconds in a Year?

Dimensional analysis can be used to determine the number of seconds in a year by converting the unit’s step by step using known conversion factors. Here’s how it can be done:

Step-by-Step Process:

1. Start with the time in a year:
   There are 365 days in a common year (or 366 days in a leap year).
2. Convert days to hours:
   Since there are 24 hours in a day, we multiply:365days/year×24hours/day=8,760hours/year
3. Convert hours to minutes:
   Each hour has 60 minutes, so:8,760 hours/year×60 minutes/hour=525,600 minutes/year  
4. Convert minutes to seconds:
   Each minute has 60 seconds, so:

   525,600 minutes/year×60 seconds/minute=31,536,000 seconds/year

   Thus, a common year has 31,536,000 seconds.

   This method uses dimensional analysis to ensure that units cancel appropriately, leading to the final result in seconds.