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

Fun fact, if you cut it in half, it’s 0.500000~.

We can measure lengths that have patterns of repeating decimals. Those are called rational numbers. You know, Ratio-nal. They can be written as fractions.

But not every fraction has a denominator made of twos and fives multiplied together, which is the only way you get a nice stopping point where the rest of your decimal expansion is zeroes.