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Let's say I'm trying to measure some variable, like GDP. The unit I'm measuring this in is dollars, and the type of unit is currency. Is there a word to describe things like "currency" in this scenario?

As another example, a variable could be stomach size, the unit is kilograms, and the thing I'm trying to describe is "weight"

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At least in physics and similar disciplines, I believe the term is quanity. An example from Wikipaedia, in the entry on Physical quantity:

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Subscripts and indices of physical quantity
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Name reference: The quantity has a subscripted or superscripted single letter, a number of letters, or an entire word, to specify what concept or entity they refer to, and tend to be written in upright roman typeface rather than italic while the quantity is in italic. For instance Ek or Ekinetic is usually used to denote kinetic energy and Ep or Epotential is usually used to denote potential energy.

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