If the oxidation number of a particular atom is not known it may be deduced from the known oxidation numbers of other atoms associated with it in a molecule. For example, the oxidation state of Pu in PuO$_2^{2+}$ is not known. It is calculated as. charge on Pu in PuO$_2^{2+}$ + charges on two O's (or 4-) = charge on PuO$_2^{2+}$ or 2+ thus Pu has an oxidation number of 6+. In some cases (S$_2$O$_4^{2-}$, Fe$_2$O$_3$) the oxidation number can be fractional. Thus oxidation numbers can be negative, positive, zero or fractional. Of course the same atom can have different oxidation numbers in different molecules. An example is shown below for nitrogen
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