For the problem

(8.99 X 10^9 NM^2/c^2)(1 X 10^-6c) / (.1m)^2 = .90 N

When I put this in my calculator I did not get .90N. Am I suppose to convert the units to get the answer. Thank you for your help.

I see Nm^2/c^2 * c / m^2 = N/c

Your units appear mangled.