Balance by oxidation number method: `Mg + HNO_(3) rarr Mg(NO_(3))_(2) + NO_(2) + H_(2)O`.

Explanation

Step 1
Step 2. `Mg + 2HNO_(3) rarr Mg(NO_(3))_(2) + NO_(2) + H_(2)O`
Step 3. To balance the number of oxygen atoms and hydrogen atoms `2HNO_(3)` is multiplied by 2
Mg + `4HNO_(3) rarr Mg(NO_(3))_(2)+2NO_(2_ + H_(2)O`
Step 4. To balance the number of hydrogen atoms, the `H_(2)O` molecule is multiplied by 2
Mg + `4HNO_(3) — Mg(NO_(3))_(2) + 2NO_(2) + 2H_(2)O`