# Dividing 100% by 3 without any left

In mathematics, as far as I know, you can’t divide 100% by 3 without having 0,1…% left.

Imagine an apple which was cloned two times, so the other 2 are completely equal in ‘quality’. The totality of the 3 apples is 100%. Now, you can divide those 3 apples for 3 persons and you will get 100% divided by 3 and none left.

Is this because 1: mathematics is not real 2: there is no 1 or 2, and it’s in fact just an invention for measurements? So, in the division of 100% by 3 WITHOUT any left, is NOT accurate?

No! we can in Math and also in real life. This is similar to ask can we divide $1$ into 3 parts? And the answer is again yes. because adding $\frac{1}{3}$ three times give $1$.
Consider 3 sticks of same length. Align these three sticks and call the total length as 1 unit. Now the length of any of the individual stick is exactly $\frac{1}{3}$ unit.
Moreover you can use the number system having base 3 to remove the (apparent) incompleteness of the base-ten expression $1÷3=0.333333333...$ In the number system having base 3, the number ‘3’ itself will be written as $10$ and the number $1$ as it is.
The division $1÷3$ is now $1÷10$ which is equal to $0.1$. so you see writing (in base ten) $100÷3=33.333333$ does not mean that we cannot divide $100$ into three equal parts. What it means is that we are using a number system having $10$ base so we cannot write $\frac{100}{3}$ in decimals.