Is the percentage symbol a constant? 
*

*Isn't the percentage symbol actually just a constant with the value $0.01$? As in 
$$
15\% = 15 \times \% = 15 \times 0.01 = 0.15.
$$

*Isn't every unit  actually just a constant? But why do we treat them in such a special way then?

Well, it really depends. In Chinese schools, students are told that $100\%=1,40\%=2/5$, so % is a constant. In the UK examination system, it appears that % is treated as a unit. Students are NOT expected to write the above two expressions.
However, it is agreed around the world that you should not write something like "$250\%$ liters of water".
So it is a good idea to think of it as a constant, but not write it as a constant.
Other units like cm, mm, kg are like the basis of a vector space or something or the imaginary unit $i^2=1$. The are NOT even like usual numbers because they cannot be added together.
