Some say egg shells need to be washed and cleaned up because they are full of bacteria and may contain salmonella.
That is a myth.
Do not wash the shells before putting the eggs in the refrigerator. The shells have protective coating that safeguards the egg from spoiling and absorbing refrigerator odors.
Better yet, keep the eggs on the egg tray carton as it absorbs odor and gives moisture to eggs.
Putting the eggs on the egg trays attached on the door of the refrigerator is not good because it will expose them to drastic changes in temperature each time it is opened and closed.
Lastly, make sure to store the eggs with their pointed end facing downward as this will help to maintain the yolk and white in place.
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