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

The fact that 1/3 is a repeating decimal is an artifact of the completely arbitrary base 10 system we use to represent numbers, and has nothing to do with physical reality. If we used base 9 instead of base 10, 1/3 could just be written as 0.3, while 1/2 would be written as the infinitely repeating decimal 0.444….