What properties of squaring SI units don't I understand?

Question

Ok here is what I did:

(200kN)^2 = 40,000 kN^2 = 40MN^2 but the textbook says it is .04MN^2 so where did I go wrong?!

Answer 1

M = Mega = 1,000,000

K = Kilo = 1,000

So 1kN = (1/1000) MN

and 1kN^2 = (1/1000)^2 MN^2 = (1/1000000) MN^2

40,000 kN^2 = 40000*(1/1000000) MN^2 = 0.04 MN^2

Get it...

Answer 2

you did not square 'k'

Answer 3

Unpack the unit prefixes, as such:

(200kN)^2 = (200000N)^2 = 4 x 10^10 N^2

Now, 1 MN = 10^6 N, so 1MN^2 = 10^12 N^2

Using the proportionality of the second equation in the previous line, we get that 4 x 10^10 N^2 = 4 x 10^(-2) MN^2 = 0.04 MN^2.  

Does that make sense?