Your correction to the square of 0.4% must have been generated by one educated in the New Math, where, according to Tom Lehrer, "the idea is the important thing"(1). You corrected the original value of 0.016% to 0.16%.
Here is the proper calculation: 0.4% = 0.004, or 4x10^-3 ( I can't superscript here, so I use the conventional '^' to represent 'raised to the power of'). When you square 4x10^-3 you get 16 x 10^-6 or 1.6^-5. Since the "per cent (y)" is 10^2 x (y), the square of 0.004, as per cent, 1.6 x 10^-3, or 0.0016%.
1. "New Math" © Tom Lehrer, 1965
None declared