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.
1in=2.54cm
1lb=0.453592kg
1 second=160minute

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.

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

From there, we are ready to move on.
1 minute = 60 seconds
1 hour = 60 minutes
60 seconds×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×24 hours=86,400 seconds

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