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?
So in mathematics, as far as I know, you can't divide 100% by 3, without having that 0,1..% left....  


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. $$1÷3=\frac{1}{3}$$ 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.
Here, in a practical way – I understand all your concepts, sirs – I was using a simple calculator on my computer, and looks like mine's got a 10 decimal digit precision. Which make this possible:

9 decimal "3s"
33.333333333 * 3
= 99.999999999

10 decimal "3s"
33.3333333333 * 3
= 100

If I divide 100 by 3, it'll give me 10 decimal "3s". And this expression was valid:
100/3 * 3 = 100