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

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.
$1 \text{in"=2.54"cm}$
$1 \text{lb"=0.453592"kg}$
$1 \text{ second"=1/60 "minute}$

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.

$1 \text{cm"=0.393701"in}$
$1 \text{kg"=2.20462"lb}$
$1 \text{ minute"=60 " seconds}$

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

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.)

$3600 \text{ seconds" xx 24" hours" = 86,400" seconds}$

...and finally:
$86 , 400 \text{ seconds" xx 365.25" days} \times 4 =$
$126 , 230 , 400 \text{ seconds}$