195706.11 + 4669.53 = 200375.63999999998 ?!? WTF?

Question

I am writing a program that has to read transaction amounts from a file and add make sure that the previous balance + transactions = current balance. I have been getting errors that the accounts are out of balance because of things like this: 195706.11 + 4669.53 = 200375.63999999998, where the current balance is 200375.64. I have tried this on two different machines using JDK 1.3.1_02 and 1.4.0. Here's a program that demonstrates this:
public class DoubleTest {
     public static void main(String[] arguments) {
          double val1 = 195706.11;
          double val2 = 4669.53;
          double sum = val1 + val2;
          System.out.println(val1 + " + " + val2 + " = " + sum);
}I don't understand why this is happening! How can I trust my Java program if it can't even do simple primative arithmatic correctly?!?

Answer 1

I don't understand why this is happening! How can I trust my Java program if it can't even do >simple primative arithmatic correctly?!? I suppose you can't trust your Java program.
Computers store data in binary form base 2. Our numbering system is base 10. Conversion between base 10 integers and base 2 binary strings is rather simple, and there is no loss of precision.
Now throw in decimals. How would you store 4669.53 in 64 bits? How about 195706.11? Here's one 132.46747236823745349058436783248905789023478956072983478569879876894537906
Much more complicated, and there is a loss of precision. Not java's fault, just the way it works. If you can come up with an idea that will cover all decimals, then you, my friend, would be a rich man. I am willing to bet my left nut you can't.
Take a look at these
http://sandbox.mc.edu/~bennet/cs110/flt/dtof.html
http://www.cut-the-knot.com/blue/frac_conv.shtml
http://www.tpub.com/neets/book13/53i.htm