Term for a “unit-ed” (versus “unitless”) quantity

What is a term for the class of measured quantities that have a unit, as distinct from those that are unitless?

This term describes any quantity with a unit:

• 5.3 seconds
• \$0.00
• −17.28 metres
• 4½ apples

This term excludes unitless quantities:

• 5.3
• 0.00
• −17.28

Note that the mass noun versus countable noun distinction is not useful here; the unit-ful quantities include both mass and countable quantities, so that's not going to help distinguish.

In other words, I want a term like “unit quantity” except that has different connotation (because a “unit quantity” implies it's exactly one of something. So that's not the correct term.)

I think the modifier “dimensioned” does not apply to abstract units (like dollars) or to counting physical objects (like apples), so if that's true then dimension excludes some quantities I want to include. That would mean it's not the correct term.

(Similar to “What do you call the part of a quantity that isn't the unit”, but I'm asking for a term that only describes a quantity including the unit, and excludes quantities that have no unit.)

• You mean a dimensioned and dimensionless quantities. – Kris Oct 31 '18 at 11:37
• @Kris - Yes, or dimensional – Jim Oct 31 '18 at 22:30
• Unitful - seriously, that is what we use as opposed to unitless. And yes, dimensionless, non-dimensional, and unitless all mean slightly different things. Unitful and dimensional are likewise different. – Phil Sweet Nov 1 '18 at 1:53

I think the term you're looking for may be "concrete number", or "numerus numeratus". According to Wikipedia, a concrete number is

"a number associated with the things being counted, in contrast to an abstract number or numerus numerans which is a number as a single entity. For example, "five apples" and "half of a pie" are concrete numbers, while "five" and "one half" are abstract numbers."

However, it doesn't seem to be a commonly used word as far as I can see, although I prefer it to "dimensioned", which seems like it was just made up to provide an opposing word to "dimensionless".

Incidentally, I'm not sure if you're right about dollars and apples, I think they may be valid dimensions, although they're discrete, but hopefully a proper physicist can settle the matter.

• Thanks. So my reading of the Wikipedia article suggests that “concrete number” is still about the number, and not the number–unit quantity as a whole. Can you expand this answer to say something about the feasibility of the term “concrete quantity” or “denominate quantity”? – bignose Oct 31 '18 at 21:56
• Hi @bignose, I would disagree. The Wikipedia article (as in the quotation given) says that "five apples" would be a concrete number, while "five" by itself would be an abstract number. Thus, you need the unit (in this case, apples), to get a concrete number. Should I make that more clear in my answer or are you after something else? – Tim Foster Nov 1 '18 at 10:29
• You've convinced me; “concrete quantity” it is. – bignose Nov 1 '18 at 21:47

Kris’s suggestion of “dimensioned” is correct. The technical concept of “dimension” does include abstractions. See James Waldby’s answer to the question “What is a name for a unit of measure and value”.

(I deleted this answer after reading the answers to the Physics SE question "Are units of angle really dimensionless?")

Grammatically the nouns naming things which can be counted (such as people, bricks, grains of sand, molecules of water and so on are known as countable.

The online Oxford dictionary defines countable as

Able to be counted.

This is in contrast to nouns which name things which can only be measured such as populations, masonry, sand, water and so on.

You could also use "countable" to describe things which occur in individual units since, by definition, the nouns which name them are countable nouns.

The only reason not to use "countable" is that the dictionaries have examples which say that its opposite 'uncountable' can describe things named by countable nouns which are too numerous to be counted (such as grains of sand on a beach) as well as substances which cannot be counted because they do not occur in discrete units (such as water, or sand considered as a mass).

An alternative would be atomic

one definition of which is

Of or forming a single irreducible unit or component in a larger system.

'a society made up of atomic individuals pursuing private interests’

Neither of these words is used exclusively in the sense you require but they both have meanings which match what you want. Either would be a possible answer.

• Thank you. The question of mass versus countable nouns is not at issue here; the class of quantities I'm trying to describe includes both countable (apples) and uncountable (water) quantities, so “countable” isn't the modifier needed here. – bignose Nov 1 '18 at 0:22
• I wasn't discussing countable and uncountable nouns, merely using them as a reason for suggesting that "countable" was a possible term to use for things which occur in countable units. What is your objection to "atomic"? – BoldBen Nov 1 '18 at 15:53
• “atomic” is not correct (implies indivisibility) for uncounted, non-atomic quantities, like water or distance. While physics tells us that yes, water is atomic and even distance has an ultimate granularity, that's not what the language of measured quantities is talking about :-) – bignose Nov 1 '18 at 21:43