I have a theory about this: We group money in magnitudes of tens up to a million but then jump up from 10x to 1,000x:
1
10
100
1,000
10,000
100,000
1,000,000
1,000,000,000
That’s a huge increase but our minds like patterns so we instinctively feel that a billion must be about 10x a million and not the 1,000x it really is, thus leading to huge inaccuracies.
Much of our perception is logarithmic, which is predictable, since patterns occur from proportion of quantities. Absolute quantities are meaningless in themselves. Even ten dollars as a quantity is meaningless except through prior experience understanding the value of a single dollar. Every value except the smallest is tenfold greater than some other value of at least some consequence.
I don't really understand your initial assumption. What if someone has 10 million dollars? Would you say he has 0.01 billion?
I think that your theory has some merit, but I believe it's more apparent when we describe the people who own the money, as opposed to the money itself: A millionaire will stay a (multi)millionaire until they become a billionaire.
I think the idea is that we still think of someone who has >1 million but <1 billion as having some number of millions of dollars, rather than subdividing "millions" into "millions," "tens of millions," and "hundreds of millions." Of course we do subdivide that when we're being particular about how incredibly rich some actor is or something, but generally they all fall on the same order of magnitude in our minds.
That’s my point. We (those of us that aren’t at least millionaires) don’t really differentiate in society between someone that has a million dollars and someone that has 10 million dollars; they’re both stuck in the “millionaires” tier.
So say you are making $50,000 a year, well it’s easy to see how you or someone like you could (theoretically) get to $100,000; that’s just the next tier up. And then it’s easy to imagine someone going from $100,000 to a million because that’s the next tier up again. But once you get there, people don’t tend to think of ten million as a tier and usually not a hundred million either. The next tier in our zeitgeist after million is billion.
So people tend to think of billion being kind of the same as going from $100,000 to $1,000,000. Hence the common disconnect about just how much more money a billionaire has than the common man.