How report metal amounts as amount of their respective metal oxides?

I have performed an element analysis, and I I have calculated the amount of each metal in my sample, given in milligrams. Let's say I weighed in 10 mg of the powder. I want to see how much of that I have accounted for by the major components in my sample (those > 1-2 %).


Since my metals were not free metals in my sample, but rather as various oxides, I need to convert back to the most common oxides. This is the idea:



> 
> If I have 1 mg $\ce{Mn}$ in my sample, how many milligrams would that be if I
>  have $\ce{MnO2}$ instead?
> 
> 
> 


Should I use the number of atoms? Like this:


I have 0.002648 g of $\ce{Mn}$ = 4.82×10-5 moles = 2.90×1019 atoms. I then assume I have 2.90×1019 molecules of $\ce{MnO2}$. Going backwards, this gives me 4.815×10-5 moles = 4.187 mg. Would this be the correct way of doing it?


