How do you convert various units uses prefixes (10^3 etc)??

Physics teacher gave example of 40km/k to m/s with working as 40(10^3m) x 1/3600s = 11m/s
also,
1000mm^2 to m^2
with working as 1000(10^-3m)^2 = 10^-3m^2

Not quite sure how she's doing this. Help??

Question

How do you convert various units uses prefixes (10^3 etc)?? 

Physics teacher gave example of 40km/k to m/s with working as 40(10^3m) x 1/3600s  =  11m/s
also,
1000mm^2 to m^2 
with working as 1000(10^-3m)^2  =  10^-3m^2

Not quite sure how she's doing this. Help??

anonymous · Answer

http://en.wikipedia.org/wiki/Metric_prefix

anonymous · Answer

each prefix has a standard conversion from the SI units

anonymous · Answer

If the units are a squared variations, the conversion ratios are squared too.

anonymous · Answer

for example,      10m^2

converting to millimeter, 1 m = 10^-3 mm

                                     1^2 m^2 = (10^-3)^2 mm^2

anonymous · Answer

$$1 m = 10^{-3} mm$$
$$1^{2} m ^{2} = (10^{-3})^{2} mm ^{2}$$

followthefez · Answer

So by looking at irkiz's answer it sounds pretty straight forward, but when I come to do the problems it doesn't work!! More explanation please??

Another question was...
Convert 64 000 nm to mm
so prefix for $$n=10^{-9}$$
prefix for $$m=10^{-3}$$ (that's 'milli')

And I don't understand how to arrange these to get the answer which is 0.064mm.