the basic logic of sig figs works like this:
lets say I give you a ruler, and a disk, and ask you to calculate the area of the disk. You then measure the radius of the disk as 1.23 meters. You know the formula of the area of a circle is pi*r^2. So you go look in a book and it says pi = 3.14159265359
So then you do 3.14159265359*1.23^2 = 4.75291552562 m^2 and you turn that is as your answer. However this answer will likely be rejected because that answer implies you measured the area to that accuracy, but in fact you only measured the accuracy to 3 significant figures (1.23).. So a more honest answer would be 4.75 m^2.
Another way to phrase it is: the significant figures in your answer conveys some idea about how accurately you measured the value to a stranger who was not present when you measured it. The answer 4.75291552562 m^2 implies you used some very sophisticated equipment to measure that area, while the answer 4.75 m^2 implies you used a rather mundane process (like a ruler).
Hopefully this gives you a basic idea why it is done. The exact rules can be found here:
http://en.wikipedia.org/wiki/Significant_figures#ArithmeticThis post was edited by Azrad on Oct 29 2013 09:53pm