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the apostrophe has to come after 1980 as it's the technology of the 1980s not the technology of 1980 as an apostrophe before the s would indicate
The apostrophe in this case is not used as genitive, as Lisa suggested, but as noun plural suffix. Therefore, it refers to the entire decade. As for the sentence, 1980's seems the best option to me, since 1980's would become an adjective and technology, the noun.
How many other noun plural suffix'es or any suffix'es have apostrophe's in their plural'ization's?
1980s is being used as an adjective in the sentence, as such we shouldn´t use ´s . It is not a matter of possession.
Doris - it is a matter of possession - it is technology 'elonging to the decade
If you use the full year, it's 1980s. If you just say the decade, it's 80's.... I guess.
It's a matter of opinion beween number 1 and 2. I prefer the first for any situation where the last character of the singular is not a lowercase letter. That way, the apostrophe is more restrained to just possessive and removed letter words. Too much misuse of apostrophes and things can get confusing.