Ca(No3)2 ------> Ca + NO2 + 2O2
As you see from 1 mole of Ca(NO3)2 you get 1 mole of Ca 1 mole of NO2 and 2 moles of Oxygen.
But 1 ,mole of Ca(NO3)2 weights 164.1 g"r  
and you have only 88.2 g"r that means you have 88.2/164.1 = 0.537 of a mole.   And that will give you 1.075 moles (simply double) of Oxygen. 
Each mole (of any material) contains 6.023*10^23  atomes (or molecules) so you'll have:
1.075 * 6.023*10^23 = 6.475 * 10^23 atoms of Oxygen. 

Please note: My answer is different from John MvCann's answer.  I believe that my answer is correct.  

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John McCann

Your answer is incorrect. The molecule, Ca(NO3)2, is all that is in question here, not the productive equation. Thus the molar ratio I have indicated is the correct procedure for this problem.

 

How many oxygen atoms are present in 88.2 grams of Ca(NO3)2?

 

There is not even intimation of an equation in this question.

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