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Ah - that I think I can explain. You see, we (at least in the US) have always counted up by every three digits (because it's handy to stick in a comma once every three digits, unless you're in Europe, where they count as decimals, and stuff :) ). Each new fourth digit we tack on gets a name.

A new name, not an -illion type, would do. Using the -illion is illogical - after all, if you call 1,000,000,000 a billion where bi means two, what's it two of?

Anyway, apart from that, if you want to go in threes then why not use the metric prefixes - e.g. $1,000 = 1K$, $1,000,000 = 1M$, $1,000,000,000 = 1G$; saves writing all those noughts and avoids the fact that we are divided in our interpretation of the word billion (etc).