Problem Solving (PS) | Re: The nearest star outside our solar system is approximately 4 x 10^13

I found the same value but in a different /I think/ way and I'd like your opinion whether my method is valid.

We are told that we want to represent the distance between Earth and moon in 1cm=1/10^5 km which means that we have to adjust the current distance to satisfy this condition. That's why I went on " 4*(10^5) = x/(10^5) " which resulted in x = 4*(10^10). I plugged this into " 4*(10^13) = 4*(10^10)*y " and I found that y = the scaled down distance in km from Earth to star = 10^3 = 1.000