Question

The CGS unit of density is g/cm cube, the SI unit of density is kg/m cube. The relation between them two is
1000kg/m cube = 1g/cm cube.
If gram and centimetre are smaller than kilogram and metre respectively, why is it that g/cm cube is bigger?

Answer 1

$$\begin{gathered} CGSunitofdensity=gm/c{m}^3 \\ Weknowthat \\ 1gm={10}^{-3}kg \\ 1cm={10}^{-2}m \\ so, \\ 1c{m}^3={\left({10}^{-2}\right)}^3={10}^{-6}{m}^3 \\ So, \\ gm/c{m}^3={10}^{-3}kg/{10}^{-6}{m}^3 \\ ={10}^{-3+6}kg/m^3 \\ ={10}^{3}kg/m^3 \end{gathered}$$