How do you complete the following metric conversion problem: 3.5 mg = ? ##mu##g?

##3.5*mg-=3500*mug##. Why and how?

##1*mg=1xx10^-3*g##

##1*mug=1xx10^-6*g##

##3.5*mg=(3.5xx10^-3*cancelg)/(10^-6*cancelg*mug^-1)##

##=10^6xx3.5xx10^-3*mug=3.5xx10^3xxcancel(10^3)xxcancel(10^-3)mug##

##=3500*mug##.

Just a note on the arithmetic, ##1/10^-3-=1/(1/10^3)=1/(1/1000)=1000##. Why? Because there are a ##"thousands"## ##"one thousandths"## in ##"one"##. Confused yet? If you don't see it, then try it on a calculator.

If you can get your head around this, you can get your head around the conversion. Good luck.