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We call the quantity of more than one (singular) plural. Is there any general word similar to this for a quantity less than one (singular)?

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You're not comparing like with like. The term 'plural' is usually taken to refer to integers above 1. Numbers less than one cannot belong to the set of positive integers. And 'quantities' usually refers to non-negatives. So, as Andrew says, you're into fractions, but these do not compare with the singular / plural concept. – Edwin Ashworth Feb 7 '14 at 9:56
... and grammatically speaking, plural is anything that is not singular, and only 1 is singular. So plural is everything else, including 1.00001, 0.99999, 0, and for some speakers −1 as well. – RegDwigнt Feb 7 '14 at 9:59
... This is only a contrivance, an attempt to tie in grammatical usage with the notions involved. '3 - 4j' is part of 'everything else' in the field of number, and I'm pretty sure it has never been described as 'grammatically plural'. Grammar and reality / philosophy don't always fit together neatly. One pie is / two pies are // 0.3 pies are // no pie is / 0 pies are // -3 pies are // 3 miles is (usually). – Edwin Ashworth Feb 7 '14 at 10:24

An amount less than one is a fraction and its adjectival form is fractional.

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But that also applies to non-whole-number amounts greater than one, as well. It is not an antonym of 'plural' as was being asked. – WS2 Feb 7 '14 at 11:30
@WS2 This is the answer to the question which was asked at the time I answered it. And even now, it still answers the body of the question, although the title has been edited. – Andrew Leach Feb 7 '14 at 11:38
Well understood . – WS2 Feb 7 '14 at 12:04
This is the answer anyway … in my experience, people use fractional frequently for amounts less than one, and are substantially less likely to use it for non-whole-number amounts greater than one. – Peter Shor Feb 7 '14 at 13:14

In particular, in terms of grammatical number, English has only singular for when there is 1 or -1 of something, and plural for all other numbers.

Some other languages have forms for particular numbers other than those, and indeed English shows a trace of a dual number in words like both and some ways of treating neither, but only a trace as phrases using them will still be otherwise using just singular and plural.

Outside of grammar, for numbers between zero and one specifically, we have fractional. There are also several terms equivalent in form to singular that are more specific about the number (dual, trial, quadral).

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@RegDwigнt where it seems people mostly agree with me, so grand. – Jon Hanna Feb 7 '14 at 10:05

More than one to plural is like less than one to zero or nothing.

Because More than one dog is at least two dogs, but less than one dog is no dog. Only one describes the singular

Mathematically less than one is from ]-infinite,1[ , but mathematically you don't call more than one plural

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