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

No. You’re confusing the fundamental nature of reality with the peculiar details of our human-created numbering system. One-third is only represented by repeating decimals because we’re using base-10 numbers. There’s no good way to represent a third with base-10. However, if you use a better base numbering system like base-12, a third can be represented quite easily indeed (although, suddenly, it’s quite hard to represent one-fifth.)

The real lesson to learn is that it’s hard to represent all numbers using any system that humans have been able to create.