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

Explanation

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