The original Japanese number system is used sometimes well as a later one derived from Chinese characters. There are some details in the wiki article

http://en.wikipedia.org/wiki/Japanese_numerals

Japanese is a natural language it wasn’t invented by a bunch of people and given specific rules, it doesn’t make sense, because it wasn’t designed. It has grown organically, and has been affected by many things.

If you are a beginner, don’t worry about things like this, just learn them, the more you learn about the language sooner or later you’ll understand why.

I wouldn’t really agree they are exceptions, because with the Japanese language, if you start describing such things as exceptions you end up with so many exceptions.

As a beginner, you will need to accept some things, if the etymology of every word that doesn’t follow a rule in Japanese, or any language, has to be explained, any beginning learner, is going to get fed up. The way teachers of Japanese get round this, is calling it an exception. Which is just a way of saying shut up and learn it. Its not very honest, and maybe if the etymology of these exceptions was explained maybe it would work better, but thats not how Japanese is taught.

So really just learn hitori and futari, and hitotsu and futatsu, and as you learn the language you’ll find out why there are these exceptions, and why they aren’t really exceptions. They are only called ‘exceptions’ because Japanese learning is done by trying to force Japanese into the framework of a foreign language’s grammar. Which doesn’t work well.

If you really do want to find out more about why things liek hito and futa are used, seriously, google it, do some research, what you learn will improve your Japanese.