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It is safest to go to 6.022, however it depends on how many significant figures you're given in the original question. For example, if you were given 5 significant figures in the original question, you would probably want to go to at least the 5th significant figure in Avogadro's number (6.0221). Whenever you're unsure though, it never hurts to use more significant figures rather than less in your calculations!
I've mostly seen people use either 6.02 or 6.022 so I usually use 6.022 since it's the more accurate of the two, but as stated above the more accurate the better as you would want to try to use as many as the sig figs you want in your final answer. (I think most questions would ask for 3 sig figs if like the class/ book examples so 6.02)
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