I have the value 30, which is a unit-less or dimension-less value. To convert this to a "unit-ed" value, I append the "ms" suffix (or more formally, multiply the dimensionless value by 1ms), giving me the value "30ms" or "30 milliseconds".

Is there a name for this process of converting a unit-less value to a unit-ed one? Off the top of my head, I can think of the non-standard "unitize", but I'm wondering if there is a standard word.

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    It makes no sense. If the number is unitless, how do you know what units to give it?? – Hot Licks Apr 6 '20 at 18:19
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    When I used to teach maths, I'd stress that we'd drop units (once we were sure there were no mixed units) and use a purely numerical model when performing necessary calculations ('physics' used to use an overly complex strategem). We'd add a caveat (working in m, s) etc. At the end, we'd convert back from pure numbers to the physical measure (eg, 4.23m; $34.56). Units and algebraic unknowns do not mix well in complex calculations. – Edwin Ashworth Apr 6 '20 at 18:24
  • You are essentially multiplying the unitless number 30 by the unit 1 m. If you reverse this you express it as multiplying the unit 1 m by the the unitless number 30. This is like starting with 1m and adding 1m to it 29 times. – Walter Mitty Apr 6 '20 at 19:07
  • To be a hair less sarcastic, you are annotating the numbers. – Hot Licks Apr 6 '20 at 22:02
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    The number is always unit-ed, now you’re just showing it – Unrelated Apr 8 '20 at 13:54

I don't think I've heard it used in quite this way, but I would say dimension.

This is an extension of the OED's definition 2 (for the verb):

transitive. To mark the dimensions on (a working drawing, diagram, or sketch). Chiefly in past participle and participial adjective.

So, "Having completed the calculation with pure numbers, we dimensioned them for the report".

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    I won't add another answer, but Wiktionary has << dimensionalise/ize (third-person singular simple present dimensionalizes, present participle dimensionalizing, simple past and past participle dimensionalized) Verb (transitive) To provide with dimensions >> I'm not sure I'd use this for writing the final answer in yen. – Edwin Ashworth Apr 8 '20 at 15:38
  • The iWeb corpus has 3 instances of dimension as a verb - all are clearly the OED's definition. It has no instances of dimensionalize, but GloWbE has 7, from N America and Singapore/Malaysia. I can't clearly work out what any of them mean, but I think they are marketing-speak for "embiggen". – Colin Fine Apr 8 '20 at 18:55
  • It should be emphasised that dimensioning in this sense is merely a matter of marking, that is of writing something down. The word 'converting', used by the OP, is misleading here, as it leaves an impression that this is a mathematical operation of some kind (which is why @Hot Licks initially commented that the question made no sense), while it is, in fact, only a matter of making explicit something that has been understood to be there all along (as pointed out by @Unrelated). – jsw29 Apr 8 '20 at 22:44


to characterize by naming an attribute - merriam-webster

In this example, you are naming the "units of measurement" attribute

  • Could you add an example from life where the term is actually used in the 'convert from a unit-less quantity to a unit-ed quantity' subsense? I've never seen it used this way. – Edwin Ashworth Apr 8 '20 at 13:56

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