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

We start by establishing a value for X.
X = 0.99… (repetend)

We then multiply both sides by 10.
10X = 9.99…

We then subtract 1X from both sides, but on the left side, using X, and on the right, X’s value. This is still equal, and thus mathematically permissible.
9X = 9

We then divide both sides by 9.
X = 1

If X=0.99…, and X=1, 0.99… must necessarily equal 1.
0.99… = 1

By extension, if we divide both sides by 3, we can further extrapolate that…
0.33… = 1/3

Therefore, 0.33… (repetend) is a perfect numerical representation of one third.