How do you use dimensional analysis to figure out how many seconds are in 4 years?

1 Answer
Nov 18, 2014

All there is behind the solution is the constant stream of multiplying. This is what dimensional analysis is all about. A conversion from one unit to another requires some sort of multiplier to change one unit to another.

Here is a list of these multipliers.
1"in"=2.54"cm"
1"lb"=0.453592"kg"
1 " second"=1/60 "minute"

If you want to switch these, all you need to do is to divide the non-one value with itself and the 1 to find the other, vice versa solution.

1"cm"=0.393701"in"
1"kg"=2.20462"lb"
1 " minute"=60 " seconds"

From there, we are ready to move on.
1 minute = 60 seconds
1 hour = 60 minutes
60" seconds" xx 60" minutes"=3600 " seconds"=1" hour"

24 hours = 1 day
365.25 days = 1 year (to account for leap years, the likelihood of the extra day out of 4 years is added.)

3600" seconds" xx 24" hours" = 86,400" seconds"

...and finally:
86,400" seconds" xx 365.25" days" xx 4=
126,230,400" seconds"