If I cut something into 3 equal pieces, there are 3 defined pieces. But, 1÷3= .333333~. Why is the math a nonstop repeating decimal when existence allows 3 pieces? Is the assumption that it’s physically impossible to cut something into 3 perfectly even pieces?

Question

If I cut something into 3 equal pieces, there are 3 defined pieces. But, 1÷3= .333333~. Why is the math a nonstop repeating decimal when existence allows 3 pieces? Is the assumption that it’s physically impossible to cut something into 3 perfectly even pieces?

In: Mathematics

Answer 1

It’s just something that happens when a number has a prime factor that isn’t a prime factor of the base (in this case base 10).

In a base 3 system (where you’d count like this: 0,1,2,10,11,12,20,…) 1/3 would be 0,1. 1/2 however would be 0.1111111111…