I want to convert $G$ from $\rm m^3 \:kg^{-1} \:s^{-2}$ to the units $\rm km^3 \: kg^{-1} min^{-2}$.

How can this be done?

I want to know what $6.67\times 10^{-11} \:\rm m^3 \:kg^{-1} \:s^{-2}$ is in $\rm km^3 \: kg^{-1} min^{-2}$.


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Unit symbols work identically to algebraic symbols: $$ 1\:\mathrm{kg} = 1000 \:\mathrm{m}, $$ say, or $1\:\rm min = 60 \:s$. As such, to convert from one unit set, you just substitute in the correct values of the old units in terms of the new units, \begin{align} G &=6.67\times 10^{-11} \:\rm m^3 \:kg^{-1} \:s^{-2} \\&=6.67\times 10^{-11} \:\rm (10^{-3}\:km)^3 \:kg^{-1} \:(1min/60)^{-2}, \end{align} and bash out the resulting numerical factors as required.


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