The same physical quantity, such as density, can be reported using different units. You found that water has a density of 1000kg/m^3=1g/cm^3 . Because the density of water must be the same regardless of what units you use to measure it, you can conclude that an object whose density is 1 kg/m^3 must be less dense than water. In other words, 1 kg/m^3 is less than 1 g/cm^3. If you had three different objects with densities of 1 kg/m^3 , 1 g/m^3 , and 1 kg/mm^3 , which object would be the most dense?

A cubic meter is equal to 1,000,000,000 cubic milimeters, 1 kilogram is equal to 1000 kilograms. First, we convert each quantity to grams per cubic milimeter:

a) [tex]1\,\frac{kg}{m^{3}}\times \frac{1,000\,g}{1\,kg} \times \frac{1\,m^{3}}{1,000,000,000\,mm^{3}} = \frac{1\,g}{1,000,000\,mm^{3}}[/tex]

b) [tex]1\,\frac{g}{m^{3}}\times \frac{1\,m^{3}}{1,000,000,000\,mm^{3}} = \frac{1\,g}{1,000,000,000\, mm^{3}}[/tex]

c) [tex]1\,\frac{kg}{mm^{3}}\times \frac{1,000\,g}{1\,kg} = 1000\,\frac{g}{mm^{3}}[/tex]

A greater density means that an object is more dense, therefore, the object that is the most dense is 1000 grams per cubic milimeter.