I've come around a great article that manages to explain floating point numbers in a great way. Forget all that you tried to learn in school and give a thorough read to this post, courtesy of Fabien Sanglard.

Explaining floating point numbers relying on the concept of window and offset is certainly a novel idea that makes things super easy to figure out; teachers, time to update your slides.;-)

Fabien is the respected author of Game Engine Black Book: a great technical dissertation about, well, game engines.