# Math notations: percent sign in arXiv (via [arXMLiv 2020](https://sigmathling.kwarc.info/resources/arxmliv-dataset-2020/))

Some quick statistics on the presence of the `%` character in a normalized plain-text version of the corpus:

7,055,855 matches
610,543 files contained matches
1,570,012 files searched

In other words 38\% of arXiv appears to contain a use of the character, with an average of 11.5 uses per document, when used.

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From a manual sample of ~200 articles, it appears `%` most often denotes "percentage", but that sample is not representative, and already has one exception (`modulo`). Also note that even in the cases with a "percentage" meaning, there are some grammatically interesting cases.

| meaning | use | source |
| ------------------------------------------------- | --------------------- | ------------------------- |
| percentage<br> over expression | $( 0.5 \pm 0.3 ) \%$ | [arxiv:0904.3774](https://arxiv.org/abs/0904.3774) |
| percentage<br> over negative number | functions, at $-0.4 \text{ to } -0.6\%$ | [arxiv:0904.3998](https://arxiv.org/abs/0904.3998) |
| percentage<br> over range | account for $∼ 30-50\%$ of the total mass | [arxiv:0904.4784](https://arxiv.org/abs/0904.4784) |
| range over percentages | $10\%-13\%$ uncertainty | [arxiv:0904.1203](https://arxiv.org/abs/0904.1203) |
| table cell datatype [unit] | $\mathcal{E}_P [\%]$ or $(\%)$ or $\delta/\%$ | [arxiv:0904.4342](https://arxiv.org/abs/0904.4342)<br>[arxiv:hep-ph/0506110](https://arxiv.org/abs/hep-ph/0506110)|
| percentage in chemical equation | ${ }^{4} \mathrm{He}+5 \% \mathrm{C}_{4} \mathrm{H}_{10}$ | [arxiv:0904.1667](https://arxiv.org/abs/0904.1667) |
| [atomic percentage](https://en.wikipedia.org/wiki/Atomic_ratio) | $\approx 4 \text{ at. } \% \text{ of } \mathrm{Mn}$ | [arxiv:0904.0297](https://arxiv.org/abs/0904.0297) |
| [percentage by weight](https://en.wikipedia.org/wiki/Mass_fraction_(chemistry)) | $wt\hyphen\%$ or $wt\%$ | [arxiv:1307.2138](https://arxiv.org/abs/1307.2138) |
| percentage as set element | $\{ 2 \% , 4 \% \}$ | [arxiv:1804.02749](https://arxiv.org/abs/1804.02749) |
| modulo | $\boldsymbol{Z}_{t}=\left\{\begin{array}{ll}\boldsymbol{Z}_{a} & \text { if } t \% 2=0 \\\boldsymbol{Z}_{b} & \text { else }\end{array}\right.$ | [arxiv:1804.11027](https://arxiv.org/abs/1804.11027)

### Aside: in programming

| meaning | use | source
|:---|:--- |:---|
| [Mathematica alias for last result](https://reference.wolfram.com/language/tutorial/BuildingUpCalculations.html) | `%+1` or `%n`, or... | [arxiv:1307.6925](https://arxiv.org/abs/1307.6925)
| [modulo](https://en.wikipedia.org/wiki/Modulo_operation#Notation) | ` x % 2 ` | |
| [formatting spec](https://realpython.com/python-f-strings/#option-1-formatting) | `ratio=%f` | [arxiv:math/0506626](https://arxiv.org/abs/math/0506626)
| matlab comment | `x_e = x ( ind_e ); %restriction - all` | [arxiv:1911.03973](https://arxiv.org/abs/1911.03973)