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There are already other notations, like scientific notation which only needs a few digits to represent e.g. 2.3 * 10^8. Not to mention hexadecimal or even base-32 which is used in Bittorrent magnet links https://en.wikipedia.org/wiki/Magnet_URI_scheme#URN.2C_conta...

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Good idea to mention the scientific notation. As it really is different from the positional notation. You can express some numbers in a shorter way then in the positional notation. Thats pretty nice. A variable length encoding with compression.

As for different bases: I consider these very similar to base 10. Maybe we will use base X in a million years, but that wouldnt be a big surprise. I was more thinking about a revolution like from "............." to "13".

Well the notation lets you tell how specific you are being about a number. Instead of saying "about 1,000" you can say 1 * 10^3 or 1.00 * 10^3 which give different amounts of information. So it's not exactly the same as base-10. And if you're talking about really big numbers, it's nice not to drag all those 0's around. It's just as big a step from .......... to 10 as from 10000000000 to 10^10.

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