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

Question

Roman Hogan · Accepted Answer

Behind the solution is nothing but a never-ending stream of multiplying. This is the essence of dimensional analysis. A multiplier is used to change one unit to another when converting from one to another.
Here is a list of these multipliers.

1 in = 2.54 cm

1 lb = 0.453592 kg

1 second = \frac{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 \times 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 \times 24 hours = 86, 400 seconds

Hence:

86, 400 seconds \times 365.25 days \times 4 =

126,230,400 seconds

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

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