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I have a noun, "second", that I need to make possessive in the sentence,

It's like having a second's slower reflexes.

When I make it plural, the apostrophe comes after the s.

It's like having two seconds' slower reflexes.

However, my noun is actually a quarter second. You only use the singular noun when there is exactly one of it, so you use the plural for zero and fragments of the noun.

They finished the task with zero seconds remaining.

They finished the task with .25 seconds remaining.

Since the noun in my sentence is plural, does that mean that for the possessive the apostrophe comes after the s, or since it is not more than one, does it come before the s? (My intuition says it comes after.)

It's like having a quarter seconds' slower reflexes.

It's like having a quarter second*'s* slower reflexes.

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The possessive apostrophe comes before the s. If you look at your sentence:

It's like having a quarter second['s or s'] slower reflexes.

There is a give away that you're actually talking about a singular thing, and not a plural. That is, you write "a quarter second". If you were writing "0.25 seconds" that would be different, but "a quarter second" is singular. It's not a "second", it's a "quarter second", which I would guess has come about through deletion of "of a" between quarter and second and gradually been normalised.

So the correct placement of the apostrophe is before the s:

It's like having a quarter second's slower reflexes.


Note:

You also have the option to not use the possessive at all and treat "a quarter second" as a noun adjunct:

It's like having a quarter second slower reflexes.

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