Hello Mike,

One of the very first posts on Mathematica.SE was on a similar topic:

http://mathematica.stackexchange.com/questions/16/can-mathematica-propose-an-exact-value-based-on-an-approximate-one

Be sure to look at all answers (not just highly voted ones), and follow the links. I asked a similar question on MathGroup a few years ago which also has interesting answers:

https://groups.google.com/d/msg/comp.soft-sys.math.mathematica/vq-MBdu51RI/lvNoiwHUPv8J

It was inspired by Maple's identify() function.