Question

What are the oxidation numbers in the compound $H_2{O}_2$?

Answer 1

You assign oxidation numbers to the elements in a compound by using the Rules for Oxidation Numbers.
The important rules for this problem are:

1. The oxidation number of H is +1, but it is -1 in when combined with less electronegative elements.
2. The oxidation number of O in compounds is usually -2, but it is -1 in peroxides.
3. The sum of the oxidation numbers of all the atoms in a neutral compound is 0.

The oxidation number of H is +1 (Rule 1).
If you know that $H_2{O}_2$ is hydrogen peroxide, you can immediately assign oxygen the $ON=-1$.
If you don't know that $H_2{O}_2$ is hydrogen peroxide, you can use Rule 3.
The oxidation number of H is +1. For two H atoms, the sum is +2.
Since $H_2{O}_2$ has no charge, the total oxidation number of the two O atoms must be -2.
The oxidation number of one oxygen atom must be -1.