Science Density Review: What I Think Density Is, Was, and What I Want To Know More! (Phew! Long Title)

                                                     Density Review   

  What I used to think density was, was the pressure in a solid, liquid, or gas. I also had a second thought, I also thought how hard the object was. 
Now I know that density is the amount of atoms in a space. To get density you need to divide mass by volume. Example: 4 grams = mass 2 grams = volume 4/2 = Density 2g/cm3. I also know that density will never change. If you have clay and you break it in half the density will still not change because it is a physical property. Water has a density of 1g/cm3 so if you have a object that has a density of 3 it will sink in water. So if you have a object that has a density of 0.6 it will float in water. 
What I want to know now more about density is, why is it mass/volume why can't it be volume/mass? Why does it have to be the amount of atoms? Those are my thoughts on density.