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Avogadro's number (6x10^23) represents the number of atoms/electrons/molecules in a mole of that substance. You'd want to use it to either convert atoms/electrons/molecules to moles or vice versa
Normally you'd want to use it when converting some other unit measurement into atoms/molecules or the other way around (1 mole of anything = 6.022 x 10^23). It's also included in some of the equations we use, but that just means you need to plug it in with the rest of your values. I think the main thing is understanding how it can convert a mole of an element/molecule into how many little parts there are in it.
The vast majority of the applications of the constant are in problems relating to stoichiometry. The units for the constant (which is used to find number of atoms, as represented by N*subscript A* on the constants and equations sheet) are inverse moles. Therefore it is used when converting between the number of moles and the number of atoms of a particular substance.
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