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

I’m addition to the various answers on the math side of this question, I thought I’d chime in on the physical aspect. Simply put, you can’t split an object into 3 equal pieces. There’s always some level of tolerance when cutting pieces, even if that tolerance is really really small. To use the marbles analogy: if you have 10 marbles, you’d end up with 3, 3, and 4. In this case the tolerance is pretty large. Now imagine if you have 10,000 marbles. Same problem, but now that one extra marble makes less of a difference because there are 33,333 others in each pile rather than just 3.