Darling! Apostrophes aren't as slippery as olives in a martini glass. The rules are cut and dry (as vermouth)!
PLURAL: She was born in the 1960s.
When we're talking about decades, no apostrophe is required. It's a plural, such as cats, days, manuscripts. No apostrophe.
ABBREVIATION: She was born in the swinging '20s.
For abbreviations of decades, we will introduce the apostrophe, which acts similarly to the apostrophe in a contraction: "can not" to "can't." It replaces missing material (letters or numbers).
If you can't remember this rule, you could also simplify and say, "She was born in the sixties."
POSSESSIVE: He wore a 1980s' hairstyle.
In the above example, 1980s' is plural and possessive. It's possessive because the hairstyle is being attributed to the 1980s. (Note: the apostrophe is after the "s.")
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I'm Coreen, and I am a copy editor, writer, instructor, digital marketer, and student of PR and Communications for organizations doing positive work in the world.