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

Define the item as having length 3. Then you can partition it into three pieces of length 1.

Define the item as having length 1. Then you partition it into three pieces of length 1/3=0.333…

They’re all real numbers. The last one is a real number too. Don’t get hung that it’s a repeating decimal. That’s a consequence of base 10 here.