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I typically don’t use an apostrophe with plurals in any situation, but I always assumed that the use of an apostrophe in constructions like acronyms:

Forty BA’s were given out to students this year.

or numbers:

Though the greatest period instability occurred during the 1950’s when. . . .

was more or less ok. I would personally use BAs and 1950s here, but I've never thought the apostrophe in this case was necessarily “incorrect”. What say ye?

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@ghoppe: Thanks for the links! – treeface Feb 22 '11 at 3:59
It's a style issue. If you were born in the 1920's you use the apostrophe. If you were born in the 1960s you don't. – Hot Licks Jan 13 at 19:58
up vote 5 down vote accepted

My answer focuses on the header question about decades—which is the question that most readers will probably expect to find answers to here. With regard to decades expressed in numerals rather than spelled out in letters, some style guides recommend omitting an apostrophe, while others recommend including it. For example, from The Chicago Manual of Style, fifteenth edition (2003):

9.37 Decades. Decades are either spelled out (as long as the century is clar) and lowercased or expressed in numerals. No apostrophe appears between the year and the s.

the nineties

the 1980s and 1990s (or, less formally, the 1980s and '90s)

The Associated Press Stylebook (2002) adopts a rule very similar to Chicago's:

decades Use Arabic figures to indicate decades of history. Use an apostrophe to indicate numerals that are left out; show plural by adding the letter s: the 1890s, the '90s, the Gay '90s, the 1920s, the mid-1930s.

The Oxford Guide to Style (2002), while differing with Chicago and AP on capitalizing the spelled out decade name (OUP prefers this) and on using abbreviations like '60s (OUP condemns this), it agrees with Chicago that the plural numeral form should be spelled without an apostrophe before the s:

To denote simple ten-year spans OUP style prefers, for example, 1920s or 1960s to nineteen-twenties or nineteen-sixties. To denote decades of a specific character (say, the Roaring Twenties, the Swinging Sixties) OUP prefers Twenties or Sixties to '20s or '60s.

But Words Into Type, third edition (1974) takes the opposing view:

In referring to decades, the sixties or the 1960's is generally preferred (not '60's, '60s, 60's, or 60s; the last form is used occasionally for ages of persons).

The New York Times Manual of Style and Usage (1999) agrees with Word Into Type about the apostrophe, although about little else:

decades should usually be given in numerals: the 1990's; the mid-1970s; the 90's. But when a decade begins a sentence it must be spelled out. [example omitted]; often that is reason enough to recast the sentence.

Clearly the question of how to render a particular decade in print is a style issue on which reasonable style guide may differ. Follow the one you have to follow, or choose the one you like.

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No idea where this answer came from and why it's suddenly become so popular, but it's a great answer. I'm switching the accepted answer to this one. – treeface Jan 15 at 23:28

Not an easy question. With dates, the rule is simple: no apostrophes. It's "1960s" and so forth.

The apostrophe is needed when it serves to avoid confusion: She earned all A's and B's.

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I think when referring to the entire group of years that make up an entire decade (and thus indicating plurality), the proper form is 1920s without the apostrophe because you are essentially stating the following: "all the years that make up the decade which begins with the year 1920" when you use this construction.

When trying to indicate that something belongs to a particular decade, you may use the apostrophe to indicate possession. For example, the apostrophe in the phrase "1920's music" would imply that you are referring to music that was composed, published, recorded, or popular during the decade which begins with the year 1920. In this case, the music belongs to the decade.

As others have said previously, the apostrophe is a way to indicate that something in a word is missing. In one case, it may indicate the omission of numbers (ex. '20 instead of 1920). In another case, it indicates the omission of words which may be used to expression possession (ex. 1920's music instead of "music that was recorded in the decade that began with the year 1920). It is never, never, never used to express plurality.

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Based on the rule of word contraction, like in "aren't", the apostrophe replaces one or more subtracted letters, which means the decades can be expressed as "the 1920s" or "the '20s", meaning that the apostrophe is used to show the subtraction of the "19" prefix.

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I'm not sure that answers OP's question. – Kaiser Octavius Jun 17 '13 at 13:38
What "rule of word contraction"? There's nothing contracted in O'Reilly or Qur'an or "the gate's hinge" or mus'haf. – Jon Hanna Jan 14 '15 at 10:22

The style sheet I received when I was working on texts for publishers suggested 1920s, but did not claim that 1920's was incorrect. Writers need to be aware that all magazines, newspapers, and publishers have their own style sheet for many of these questions and that there is no unanimity among them. BTW, the answer above that 20's is correct because the apostrophe indicates something missing as in a contraction is incorrect. One of the reasons apostrophe use is so confusing is because using 's to indicate the plural form of things like decades, or grades on report cards has always been acceptable. It is this rule that confuses writers who then incorrectly use the 's for plurals such as apple's and other nouns such as family names (the Smith's). It is to avoid this error that style sheets recommend the lower case s as the plural for I received 4 Bs on my report card, but if I am an A student, it is context that explains that As stands for grades not the comparison.

Best solution in such situations--find an alternative. Write the Roaring Twenties.

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Are you sure that it is this that confuses people into using 's in plural forms instead of -s? Somehow I doubt that. – Kaiser Octavius Jun 17 '13 at 13:54
I don't see anything in either answer above that states "20's is correct because the apostrophe indicates something missing". One answer does state that the '20s (apostrophe before the 2, not before the s) is a contraction of (usually) the 1920s - and that is perfectly correct. – TrevorD Jun 17 '13 at 15:23
Incidentally, expressions like the answer above are unhelpful on SE because the sequencing of answers varies according to their scores. – TrevorD Jun 17 '13 at 15:25

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