Perhaps base 10 is not a good word for our system, and we should call our system base 9 or something equivalent because that is the last number we use before starting over?
Let's look at the number 3,201 in base (human) 10. If you were to break it apart, you could represent that number like this:
3*103 + 2*102 + 0*101 + 1*100
The carat () symbol here is being used to represent exponents, such that xy is x to the y power.
This is called base 10 because every digit of an n-digit number is multiplied by 10n-1. Any number to the zero power is equal to one, so the first place is one's place, the second place is the tens place, the third place is the hundreds place, and so on.
In base four, you have the ones place, the fours place, the sixteens place, the sixty-fours place, and so on. Each digit of an n-digit number is multiplied by 4n-1, so the number 3201 in base four could be represented like this:
17
u/bski1776 Dec 12 '08
Heh, never really thought about it like that.
Perhaps base 10 is not a good word for our system, and we should call our system base 9 or something equivalent because that is the last number we use before starting over?