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

Question

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
• 4½

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.

Candidate terms already tried

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.)

Answer 1

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.

Answer 2

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”.

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

Answer 3

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.