Is it correct to say 1960s?
It is acceptable to spell out a decade span and to abbreviate a decade span on second reference. When abbreviating a decade span, put an apostrophe before the numbers (facing the correct way) but NOT before the “s.” A decade cannot possess anything! NOT 60’s, but ’60s. The nineties were a great decade.
How do you write 1960s and 70s?
Actually, you *do* need an apostrophe in ’50s, ’60s, ’70s, ’80s, etc. It just goes before the numeral (replacing the “19”) instead of after the zero. Periods, however, _should_ be placed inside quotation marks at the ends of sentences. My manager seems to think an apostrophe makes things plural.