# Why is mass fraction always abbreviated wt% and not ma%?

In most geology papers, major elements chemical analyses are expressed as mass fraction of oxides, i.e. SiO$$_2$$ 64.2 wt%, K$$_2$$O 4.3 wt%, etc. The mass fraction unit is always abbreviated as "wt%". Even my bible when it comes to igneous rocks classification/terminology (Le Maitre et al. 2002) uses it.

What bothers me is that "wt" refers to the weight, which is a force, not a mass. I know it is common usage to use "weight" to refer to the mass of an object, but when writing science shouldn't we be more accurate and use the proper words? Molar and volume fractions are abbreviated mol% and vol%, respectively. Isn't it time for the "ma%" or "mas%" revolution? If I write "mas%" in a paper, will the reviewers/editors accept it?

## 4 Answers

This is because of historical inertia.

Yes, you are correct that "mass" is technically more correct than "weight". However, because these are percentages, it does not matter. There are no units. A rock that has 50 weight% SiO2 also has 50 mass% SiO2, regardless of the planet (i.e. g) you are in.

Regarding using "ma%" - I have never seen it and it would be confusing, especially since "ma" will probably be interpreted as the unit "milliannum" which is weird. Using "mass%" would be better, but "wt%" is only 3 characters compared to 5 so there's the issue of laziness. I have seen papers using "mass%" and that's fine, and I wouldn't object to such usage if I were to review a paper.

That said, geologist often weigh rocks. Yes, the numbers are mass. But the action itself is "weigh". Go figure.

• In my case the bulk rock analysis was done by spectrometry, so the action was measuring a proportion of atoms! But it's true that before the analysis I weighted a certain amount of powder to dissolve... Thanks for your insight anyway, I'll try the "mass%" and see how it goes. – Jean-Marie Prival Feb 24 at 9:23

My speculation is that if you try to use ma% or mas%, you will be asked to change it to wt%, because what you are proposing is not yet standard usage.

If I came across ma%, my initial though would be "what does that mean". My second thought would be, "does it mean milli annums percent?", (thousandsths of a year percent) - which would be meaningless to me.

If you want to introduce a new terminology, I would suggest not using abbreviations. Instead, use mass% to make things clear.

You can try to lobby the body responsible for units used in the Metric system to change from wt% to something else, but until a change has been adopted, which may take years, keep using standard notation.

My speculation about the continued use of weight percent (wt%) is due to English language usage and the persistence of habits.

For a very long time, with English, it has been common practice to say something like "how much does that weigh". It rolls off the tongue easily. At a doctor's surgery people will be asked "how much do you weigh", not "what is you mass". Most people don't know what mass means in an every day scientific context, but they do know about weight.

• Even if a change is adopted, that may mean nothing. ISO officially advises against the term "wavenumber", stating we should use "repetency" instead, and see how successful that one has been... – gerrit Jan 10 at 11:12
• "what you are proposing is not yet standard usage": I understand, but it will never become standard usage if we don't start to use it at some point... – Jean-Marie Prival Jan 10 at 11:40
• @Jean-MariePrival: I've edited my answer to include: If you want to introduce a new terminology, I would suggest not using abbreviations. Instead, use mass% to make things clear. – Fred Jan 10 at 17:58

Conventions, whether set by standards or by common usage, are not always in line with the most intuitive or the "most accurate" approach. Would for example that the electrical engineers would stop writing that current flow is in the direction of motion of positive charges rather than that of electrons, we will all be "more accurate".

As has been noted, the relative values of weight percent are the same as those for mass percent. I would add, this is true whether we are on earth, on the moon, or on Jupiter. Only when we are in a non-inertial frame (no $$g$$ for the conversion), do we have any reason to question the truth of the convention.

The term wt% is used in a diverse number of communities beyond the area of your focus (geology), including especially chemistry, chemical engineering, and materials science/engineering. The term is strongly ingrained in those communities. The convention is only "not accurate" in the sense of corrupting the semantics, not in the sense of corrupting the accuracy of any calculations we do with the numbers. Staying with the convention of wt% will make your reports readable across the larger communities. Indeed, switching to your own preferred convention of ma%, essentially just for the purity of semantics, may cause more confusion or aggravation for others in your own community as well as in the outside communities. They will have to "think twice" to translate the new notation to their own.

Otherwise, you are almost akin to a lone wolf crying in a big forest on this one. Allow the terminology to evolve on its own. Alternatively, become active in professional societies such as IUPAC or ASME or ... where such decisions start to take root to action, make your voice heard, and see what you learn at that level.

• I do attach importance to semantics. And from reading old scientific literature, I've seen terminology evolve. For instance we used to say "basic" and "acid" rocks, now we say "mafic" and "felsic". So I don't see why we could not start changing this particular convention. – Jean-Marie Prival Feb 25 at 8:27
• @Jean-MariePrival I've amended my post to address this question. You are not wrong to ask why we could not start to change the current convention. You may however be overly idealist to believe that anyone else truly cares enough to change it relative given the effort required versus the return. – Jeffrey J Weimer Feb 25 at 14:52
• Thanks! I've been looking at the IUPAC following your edit, see my answer below. In summary: there was actually a decision made about this, but nobody follows it. I guess you're right, I'm too idealist... – Jean-Marie Prival Feb 25 at 16:29

(I'm posting this as an answer because it's too long for a comment.)

Jeffrey's answer got me looking at the recommendations of the International Union of Pure and Applied Chemistry (IUPAC), "the world authority on chemical nomenclature, terminology [...]." They published Quantities, Units and Symbols in Physical Chemistry, AKA the "Green Book". Section 3.10.1 (page 97) reads:

Fractions such as relative uncertainty, amount-of-substance fraction $$x$$ (also called amount fraction), mass fraction $$w$$, and volume fraction $$\varphi$$ (see Section 2.10, p. 47 for all these quantities), are sometimes expressed in terms of the symbols in the table below. [...] These multiples of the unit one are not part of the SI and ISO recommends that these symbols should never be used. [...] Even then, the use of an appropriate SI unit ratio may be preferred. Examples: The mass fraction $$w$$ = 1.5 $$\times$$ 10$$^{−6}$$ = 1.5 mg/kg.

So, I guess we should not write a rock has a SiO$$_2$$ content of 64.2 wt%, but rather that the SiO$$_2$$ content is 0.642, or better 642 g/kg, which looks weird. I've never seen this written anywhere. The funny thing is that on the next page (p. 98), there is another table which says that ppm, ppb... are deprecated and should be replaced by µmol/mol and equivalents. Again, I've never seen this written anywhere, all papers use ppm.

I guess the conclusion of this is: there are conventions, and then there is common usage, and sometimes usage goes against convention. I'm OK to follow the common usage, but I feel bad for the commissions working hard on proper terminology, publishing entire books about it, if nobody follows them in the end...

• Three comments: First, any value that is reported without units is ambiguous. So at least use the second convention for mass fraction. Secondly, ppm ... are standard terms world of semiconductor device production where they mean mass of component per total mass (not moles per mole). What groups such as the environmental chemists do to ignore the assumptions behind these values is often rather amusing. For that reason alone I support IUPAC's recommendation -- it brings clarity. Finally, I would write the units as g X/kg total and $\mu$mol X/mol total (pedantic as I tend to be). – Jeffrey J Weimer Feb 25 at 16:46