Whether you purchase onions that come in open mesh bags or are purchased in bulk, make sure to examine each onion (as much as possible). One spoiled onion can spread decay to the whole bunch.
Selecting Onions
The neck of the onion should be tightly closed and dry, but avoid onions with a woody center in the neck. The entire onion should be firm, avoid those with soft spots. Dark powdery patches just under the skin indicate mold that will eventually spread and damage the flesh.
Onions with a greenish tinge have been exposed to too much light. You will want to avoid these onions since it does affect the taste.
Storing Onions
In storage, onions need air circulation and should be kept in a cool dry spot. The refrigerator is generally not a suitable spot since there is too much humidity.
One of my favorite tips for onion storage is to store them in clean pantyhose. Simply cut the leg off the pantyhose, drop an onion into the leg (down to the foot area), tie a knot above the onion. Drop another onion in the leg, knot, and continue the process until the leg is full. Then hang your string of onions in a cool, dry place. When you need an onion, simply cut a slit in the pantyhose and remove an onion.
Check out this great example:
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