Translating m^2/C^2 to cm^2/μC^2 (couloumbs law)

[lozzajp]

I am hoping I have this right but want to make sure.
I have 9x10^9 x N x m^2/C^2 and want to use units of cm and μC (micro)

9x10^9 x N x 1m^2/1C^2 x 10000cm^2/1m^2 x 1C^2/1x10^12μC^2
9x10^9 x N x 10000cm^2/1x10^12μC^2
90 x N x 1cm^2/1μC^2

Have I got that right? Havent fallen into any traps or made a mistake?

Thanks for any help, hope I've written it well enough to see what's going on.

 

[Mute]

Looks good to me.