A "fifth" was a unit of volume, representing a fifth of a gallon, that used to be used in the US to measure liquor.
A liter weighs a kilogram which is 2.2 pounds (H20). A gallon weighs 8 pounds (H20). There are five "fifths" in a gallon, so a fifth is 8/5 pounds, or 1.6 pounds. There are 2.2/1.6 or 1.375 fifths in a liter.
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