How to convert 1 kilogram/cubic meters into grams/cubic centimeters

How to convert 1 kg/m³ into g/cm³

$$1\ \dfrac{\ kg}{m^3}} \\ \\ =\left( \dfrac{1\ kg}{m*m*m}} \right) * \left( \dfrac{1000\ g}{1\ kg} \right) * \left( \dfrac{1\ m}{100\ cm} \right) * \left( \dfrac{1\ m}{100\ cm} \right) * \left( \dfrac{1\ m}{100\ cm} \right) \\ \\ = \left( \dfrac{1000}{100*100*100} \right) \left( \dfrac{g}{cm^3} \right)\\\\ = \left( \dfrac{1}{1000} \right) \left( \dfrac{g}{cm^3} \right) \\\\ = 10^{-3} \left( \dfrac{g}{cm^3} \right)\\\\ = 10^{-3}\dfrac{g}{cm^3}$$

$$\boxed{ 1\ \dfrac{\ kg}{m^3} = 10^{-3}\dfrac{g}{cm^3} }$$