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 reason is because we use base 10 as our counting system. It’s totally arbitrary. If we used base 12, 1/3 would be written exactly as 0.4. Not 0.4444…just 0.4.

Repeating decimals aren’t some kind of philosophical conundrum. They’re just the result of what number system we choose to use.