Suppose we have quantities q 1 , q 2 , … … , q n , where the units of q i contain length raised to the power c i . If we originally measure length in meters but later switch to centimeters, then the numerical value of q i would be rescaled by a factor of 100 c i . Any physically meaningful law should be invariant under an arbitrary rescaling of every fundamental unit; this is the fact that the pi theorem hinges on.