Why do we use 10 as a whole unit when it can't be evenly divided by 3 or 6 without resulting in an infinite decimal I.e 3.3333etc.
If units of 12 were used I.e 1 2 3 4 5 6 7 8 9 ? # 10. 3.3333 would become 3.4 (10/3=3.4)
In math, I'm told, if you have an infinite, something is wrong with the equation
So using a base of ten must be an incorrect way to measure
My apologies for the crudeness of this inquiry, I just typed it out on an iPod at a coffee shop real quick, little consideration for how articulate it comes out
Most things that are meaningful in mathematics are completely independent of representation - it's important that the notation doesn't affect the result. The fact that we don't have $12$ units is just a convention, mostly based on the fact that we have $10$ fingers.
Besides, base $12$ doesn't allow division by $5$ without an infinitely repeating expansion, so it doesn't really address your objection that some numbers have expansions that don't terminate.
In fact, almost every real number has a non-terminating expansion regardless of whether you're using a system based on $10$ units or $12$.