When Pi is calculated in decimal you get a never ending remainder. Is this simply a quirk of the decimal system that wouldn’t exist if we were born with 12 fingers instead of 10?
What would happen if your used hexadecimal or unidecimal to find the value of pi. Is there a way to find a theorical base system which would produce a whole number for pi. Like base 42, for example?
In: 15
Irrational numbers are always irrational and rational numbers are always rational, as long as you use any integer as the base of your counting system.
It’s commonly said that an irrational number is one whose decimal representation goes on forever. This isn’t quite correct, since a number whose decimal representation repeats in an infinite pattern will be a rational number (and technically, if a number’s decimal representation terminates that really is just the same thing as saying it ends with a repeating zero). Whether a rational number terminates or repeats can depend on the counting system.
For example, 1/3 in base ten is equal to 0.333333…, but in base twelve it is 0.4.
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