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When notating error using the $\pm$ symbol, are the units only ever included at the end? For example:

10.2 $\pm$ 3.2 m

rather than

10.2 m $\pm$ 3.2 m

This seems to be correct though I wonder if that also applies to writing an angle in degrees. In this case, it seems better to repeat it as in,

36.8$^\circ \pm$ 1.3$^\circ$

rather than

36.8 $\pm$ 1.3$^\circ$

I am not sure where to find any kind of standard related to this.

Emilio Pisanty
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Steven C. Howell
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1 Answers1

10

It appears that none of Physical Review Style and Notation Guide, the AIP Style Manual, the IAU Style Manual, or The ACS Style Guide: A Manual for Authors and Editors, weigh in at all on this matter, so I would say it is to some extent up to personal taste.

On the other hand, the NIST Manuscript Checklist does take a position:

$$\begin{array}{rl} \text{proper:} & \text{123 g ± 2 g or (123 ± 2) g }\\ & \text{70 % ± 5 % or (70 ± 5) % }\\ & \text{240 × (1 ± 10 %) V }\\ \\ \text{improper:} & \text{123 ± 2 g }\\ & \text{70 ± 5 % }\\ & \text{240 V ± 10 % (one cannot add 240 V and 10 %) }\\ \end{array}$$

Similarly, the IUPAC guide Quantities, units and symbols in physical chemistry explicitly recommends the form $(100.021\:47\pm0.000\:70)\:\mathrm g$.

Nevertheless, actual usage is very forgiving, and you end up seeing all forms to some extent. Some recent examples from the literature:

As you can see, pretty much anything goes as long as it is clear. A lotof people do tend to use $$10.2±3.2\:\mathrm m$$ and that is perfectly clear (even though slightly discouraged). However, if there is some ambiguity, such as with $36.8°± 1.3°$, it doesn't hurt to include the extra degree symbol, or to use parenthesis as in $(10.2±3.2)\:\mathrm m$. In general, I find repeated units to just make the text wordier without doing all that much to clarify any ambiguity.

The aim of scientific and technical writing is to communicate clearly and unambiguously. As long as it's immediately clear what you mean, you're fine, and if on top of it you're concise and readable then all the better.

Emilio Pisanty
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  • When you say repeated units just make the text wordier without clarifying anything, are you saying only that you prefer $(10.2\pm 3.2)\mathrm{m}$ to $10.2\ \mathrm{m}\pm 3.2\ \mathrm{m}$, or also that you prefer $10.2\pm 3.2\ \mathrm{m}$ to $10.2\ \mathrm{m}\pm 3.2\ \mathrm{m}$? – David Z Feb 29 '16 at 17:03
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    I'm saying that I prefer $(10.2±3.2):\mathrm m$ to $10.:\mathrm m±3.2:\mathrm m$ pretty much all the time. I tend to find that $10.2±3.2:\mathrm m$ may or may not be ambiguous depending on the context; if it's ambiguous it should not be used, and if it isn't ambiguous I do find it preferable to $10.:\mathrm m±3.2:\mathrm m$. The usage $10.2±3.2:\mathrm m$ is indeed discouraged by the existing guidance (to the small extent that the guidance weighs in on this) but you do see it a lot and, unless the context makes it ambiguous, I personally don't have much against it. – Emilio Pisanty Feb 29 '16 at 17:26