# How are probabilities written in German?

I was reading over some statistics notes that one of the German universities had made available online (it is entirely in German), and I'm confused because they've written P(X=1)=0.25. That's exactly how we write decimal probabilities in English, but I was told that the commas and periods are always switched in German. So for example, your weekly salary of one thousand Euros is written 1.000 and your coffee costs you 2,00 in Germany.

Most of the notes on the Wahrscheinlichkeit document are written as P(X=1)= 1/4 (in English, we also tend to write probabilities as fractions, so those ones are easy to read as they're identical to how we write it). But I'm definitely confused about why P(X=1)=0.25 isn't written with a comma there? I couldn't find anything on Google explaining what is going on with those probabilities. Thanks!

• Also, because of the inconveniences mentioned in german.stackexchange.com/questions/62445/…, the author may just have consciously decided for themselves that it is easier to use a decimal point. Jan 25, 2021 at 15:27
• I am absolutely German, but I will often write American 1s and 7s. Who will stop me from doing so? :) Jan 25, 2021 at 15:48
• Note that while the decimal sign should be a comma in German (and a bunch of other European languages), groups of 3 orders of magnitude are spaced rather than separated by dots according to Duden. This spacing also officially starts with numbers >1e6, so at least 2 such digit group separators in a number. As others have said, we're nowadays fluent in reading decimal commas or decimal points. The one really bad exception is that I've come across .csv files that had comma both as column separator and decimal point... Jan 26, 2021 at 13:16
• 1.000 or 1,000 for 1000 are both absolutely horrible, ambiguous notations. A space or nothing at all is much safer, in any language. Jan 26, 2021 at 14:39
• I am French but we have the same situation. I grew up with commas for decimals, I usually use them as such when writing on paper. On a computer I instinctively use a dot for decimals.
– WoJ
Jan 26, 2021 at 17:50

This is not related to writing about probabilities in particular. Most probably this is just a typo of someone who is used to writing in English.

You are right, in general a comma is used as the decimal separator in German. However, in contexts where most relevant literature is in English (as in statistics / stochastics) and in documents written by people who are used to communicating in English, you might stumble across this "mistake" to write a dot instead of a comma, as it is usual in English. So, from a different point of view, this could also be classified as an anglicism in writing, rather than as a mere mistake. (This is why I write "mistake" in quotes here.) If the document consistently uses dots instead of commas, this is a strong argument that we actually face a style of writing the author chose intentionally.

As with many "mistakes", once they become common enough, a new standard develops. I would say, writing a comma as the decimal separator is still the standard in German, but maybe we happen to find ourselves in the midst of a language change process here.

• Thanks very much. The author's first and last name are German, but as you said, he may have studied in the UK or the US and become accustomed to our way. All of the decimal probabilities in the example sum to 1, which is a good sign. The document contains previous test questions with no solutions, so I can't actually check the solution for that example.
– user47528
Jan 25, 2021 at 15:00
• @Only_me This goes even further than just "may have studied in UK/US". From my personal experience as a german computer scientist: Ever since computers became part of everyone's lives, the decimal point started to compete with the decimal comma here in germany -- because lots of software wasn't localized when it started to get used here. It's even getting to the point where some germans (me, for one) are speaking "Null Punkt Zwei Fünf" and only some people above the age of maybe forty feel a pinge of "this ain't correct german" when listening to that. Jan 26, 2021 at 11:50
• I am a native german speaker and cs student and programmer. I can't tell you how often I've mistakenly used the point as decimal separator in german texts, because I use it all day when programming, communicating in english, reading in english and so on. I'd say give it a few decades, and the point will be completely accepted as decimal separator in german, too. Jan 26, 2021 at 13:25
• @Polygnome: I tend to differ. In former software, american notation was often the only option. Today, more and more software is localized. See spreadsheet software like LibreOffice:Calc or operating systems, like Linux. Only programming interfaces/languages remain English. And too few people work with programming languages. Jan 26, 2021 at 16:27
• @userunknown. But this question is a probability question and all maths/stats graduates work with programming languages like R, Python and SAS to solve our problems. When you say too few people work with programming languages, that is not the case here as any person reading this post would have needed to study probability and maths software to be able to answer my question. So Polygnome is correct; all maths students also study programming.
– user47528
Jan 30, 2021 at 9:52

I am teaching statistics too at an Austrian university1 together with a professor for statistics (I'm not a professor). And I noticed, that my colleague - although he is a German native speaker, born, grown up and living in Austria - uses his compete computer equipment in English language. And this makes sense, because the lingua franca of any modern science, including mathematics and statistics, is English.

And I also noticed, that in handwritten notes he also uses the English notation, so he writes a decimal dot instead of a decimal comma. And also in our lessons, when he teaches the students in German language, he consequently used the English notation.

This is not a problem, neither to me nor to our students. We all are used to read scientific papers in English language, and many of the students also write their bachelor or master thesis in English. They are even encouraged to write in English, because when you decide to become a scientist, this is the language you have to use to publish all your scientific papers, at least in computer science, mathematics and statistics.

But you are right: Using English decimal notation in German documents is wrong. But especially scientists who care more about correctness in their own subject than about correct language make this special kind of mistake.

At the moment these are just singular errors, and maybe it will not spread out. But it is also possible, that we just now watch the beginning of a change of how we use our language. Maybe in some decades decimal dots and decimal commas are two accepted variations which coexist side by side.

1 St. Pölten University of Applied Sciences

• I did wonder about that, because many German universities now offer a mixture of English and German classes within the same degree, so students are switching back and forth between languages as they go from class to class. I see this on CompSci curriculums often.
– user47528
Jan 25, 2021 at 22:08
• It makes sense to set the regional settings to English because it's much easier and faster to google for support when something goes wrong. Jan 26, 2021 at 14:42
• This. I studied computer science in Austria (Vienna University of Technology) and I remember that we had some (mathematics?) courses where the instructor explicitly stated that he will use a decimal point instead of a comma because it makes notation easier---for example, it allows you to use the comma as a list separator in sequences. As long as there is no ambiguity (and there usually isn't, because there's enough context), that's not a problem at all. Jan 27, 2021 at 9:42
• @EricDuminil: That's the UI language, not the regional settings. I know that because I use a (US-)English UI for exactly the reason you mentioned, but I can't stand the absurdity of the mm/dd/yyyy date format, so my regional settings are different. Jan 27, 2021 at 9:45
• @Heinzi: Thanks, you're right. That's what I meant but couldn't remember the correct description. Close enough! Also, I cannot accept that sunday is the first day of the week in my calendars. :) Jan 27, 2021 at 9:46

In school and in texts for the general public/a non-international audience, you will pretty much only find the German way of writing decimals: using a decimal comma.

At university or in similar contexts of higher education, top-level research or large international companies, a decimal dot might be used for any of the following reasons:

• the writers are used to using it in their English works
• the writers expect the readers to be used to or to get used to English usage
• the writers consciously chose to use English usage in both English and German publications so that they only need to deal with one notation
• the writers are following a style guide that requires consistent usage across all languages (especially for international companies)

Finally, it is possible that it is really just a typo and the writer intended to use a decimal comma: the two are next to each other on the keyboard.

I do want to stress though, that unlike Jonathan I do not think that the German standard of a decimal comma will change any time soon. Most of the bullet points above are people choosing for themselves to not follow standard German practice, knowing that their usage is now not a standard. I see little evidence of this catching on in any scale across the general public – especially since standard office programs sold in German default to a decimal comma.

• I am also a case of reason 3, but initially for a more ridiculous motivation: using periods makes hand-written row vectors decipherable, since you can't rely on spacing too much, there. `[1,2, 3,4]` vs. `[1.2, 3,4]`. Jan 26, 2021 at 13:49
• @phipsgabler I solve that with semicolons. I actually find [1,2; 3,4] easier to parse than [1.2, 3.4] because the semicolon looks larger, so I would probably use [1.2; 3.4] in English anyway ;)
– Jan
Jan 26, 2021 at 13:54
• @Jan but then you have a column vector.. (depending on the language) Jan 26, 2021 at 17:08
• Well for me the "standard office" programs default nearly always to the wrong notation. If I have a german text they import it in the english notation and vice versa. Jan 27, 2021 at 6:49

Another thing to consider: The German publications are getting "internationalized" more often compared to the past. It used to be the case that a lot of German research work was primarily done in German and written for a German speaking audience (in Germany, Austria, Switzerland), especially in social science, psychology etc.

There is a shift for German researchers to write their publications in English and to use the "common" English citations and formation guidelines (e.g. APA). When APA is used in a German publication, the APA guidelines for numbers are used, no matter the language of the publication. This could also be the "cause" of the punctuation in the German paper. (https://www.jcu.edu.sg/__data/assets/pdf_file/0009/680085/Numbers-in-APA.pdf)

APA Numbers

• Welcome to German.SE. Do you think it would be useful to cite the relevant part of the APA guidelines as you considered them as example? The link is fine for further research, the quote would make your answer less "somewhere there it is". I understand that APA is only one example. Jan 28, 2021 at 20:39
• I included another link for APA, I don't understand what you are reffering to with "somewhere there is". Jan 29, 2021 at 8:02
• I'm referencing to this help section , part "provide context for links" german.stackexchange.com/help/how-to-answer - the link alone is not enough, so to speak Jan 29, 2021 at 13:54