A nice article explaining the troubles of float numbers, and what effects it can have. It is talking in the case of Visual C++, but the problems are the same for other compilers.

Do You Prefer Fast or Precise?

by Jim Hogg

From the article:

Floating Point Basics

In C++, a float can store a value in the 3 (approximate) disjoint ranges { [-E+38, -E-38], 0, [E-38, E+38] }. Each float consumes 32 bits of memory. In this limited space, a float can only store approximately 4 billion different values. It does this in a cunning way, where adjacent values for small numbers lie close together; while adjacent values for big numbers lie far apart. You can count on each float value being accurate to about 7 decimal digits.

Floating Point Calculations

We all understand how a computer calculates with ints. But what about floats? One obvious effect is that if I add a big number and a small number, the small one may simply get lost. For example, E+20 + E-20 results in E+20 – there are not enough bits of precision within a float to represent the precise/exact/correct value...