Very interesting thread,
I would just like to point out that both systems were invented in Europe, just like the confusing month/day/year now used in the U.S. versus the day/month/year system used by the Brits and most other people when writing calendrical dates. Now, back to the counting problem. Interestingly enough, both methodologies have a history in France where both systems were used at alternate periods in its history. Well, here's the logic behind the American system:
1,000=thousand
1,000,000=million (basically a thousand thousand)
1,000,000,000=billion (2 sets of zeros after a thousand)
1,000,000,000,000=trillion (3 sets of zeros after a thousand)
1,000,000,000,000,000=quadrillion (4 sets " " " " thousand)
1,000,000,000,000,000,000=quintillion (5 sets " " " " thousand)
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You get the logic by now. Some other interesting numbers:
10^100 (ten to the hundredth power/to the power of 100)= googol (essentially one followed by a hundred zeros)
10^10^100= 10googol =googolplex (one followed by a googol zeros).
Hope this helps you understand our system.