This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Floating-point numbers on a computer, like java's double and float primitive types, are approximate values. There has to be a compromise between the precision of a value and the amount of memory it would take to represent it. Otherwise how could we represent a number like pi, which has an infinite number of digits? This article is a good introduction to the concepts and pitfalls of floating-point numbers. Incidentally, java provides two classes in the java.math classes for representing arbitrary-precision values, like when working with money.
Also, you might want to read up on the strictfp keyword that was added around the JDK 1.3 (I think). I'm not sure this will solve your problem...I'm pretty sure use of that keyword only guarantees that all calculations will result in the same value regardless of the platform your classes happen to be running on.
There's been a lot of time and energy devoted to doing exact calculations in computing. All you have to do is look and you'll find a lot...I think even Knuth's canon of numerical algorithms addresses this topic.