While chopped onion is kept in deep freezers for a longer time and then kept at room temperature inside an airtight container it still remains good
Keep the skin on a full half, seal it, and store it face down in the fridge.
Other half same thing but no skin.
The onion should be stored in cool, dry conditions (e.g., the inside of a refrigerator). It should not be exposed to air, as this will cause it to oxidize (i.e., react with the oxygen molecules present in air). We can combat this issue by placing the cut onion in an airtight plastic ziploc bag, or encasing it in plastic wrap. The plastic-covered cut onion should then be placed in the refrigerator, where it will preserve its freshness for up to two weeks. If you begin to notice dark spots, then the onion is beginning to spoil. These dark spots can be removed by simply slicing them off; alternatively, you can avoid spoilage altogether by freezing the cut onion in an airtight plastic encasing until its ready for use.
As with nearly all vegetables, if you want to maximize fridge life of cut raw onions, make sure you use well-maintained tools that cut cleanly - sharp knives, or if machines are used, sharp and good quality blades. Rough tools (blunt machine blades, serrated knives...) will rip the top layer of the cut pieces apart, causing more water loss, more enzymatic activity and more oxidation.
We do it this way. Cut onion amount you need off. Leave skin on the rest. Place in a small plastic butter cup like butter comes in from the store. Put on lid. Set on top shelf in the fridge door so it gets used first before starting a new onion. Chopped onion can be stores same short term in fridge door. Easy to grab & use there.