I would like to know the general method of converting between units. For example converting Joules to $\frac{g\cdot cm^2}{s^2}$
I assume it's possible because the SI unit of energy is $\frac{kg\cdot cm^2}{s^2}$ so is it as simple as going from J to $\frac{kg\cdot cm^2}{s^2}$ and then times 1000 to get $\frac{g\cdot cm^2}{s^2}$?
If so then how does one know how many J in 1 $\frac{kg\cdot cm^2}{s^2}$? Is it something you have to learn like 1kg is 1000g?