# Dezimalzahlen



## Christos1

Ι would like to ask how can we read the "Dezimalzahlen"

For instance the numbers:

*1) 5,478
2) 34,9876*


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## Arukami

Fünf Komma vier sieben acht. Vierunddreißig Komma neun acht sieben sechs. Same goes for every other number too.


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## Christos1

i asked because i read that we can express the number 4,45 as: vier komma fünfundvierzig.


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## Arukami

Well, if you want to. It's not a very common thing to do, I think.


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## lingpil

It's not very professional to say "Komma fünfundvierzig" because it's simply wrong. The decimals are not numbers "on their own". In case of 000001 you can say just "eins" because it's the only valid potence. But you can not call 6,00001 "sechs Komma eins", since all decimals are valid. If you want to use the expressions for work in a job where a more or less precision is required I recommend you the "decimal by decimal" method. Like in all languages I happen to know better, by the way.


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## Frank78

Arukami said:


> Well, if you want to. It's not a very common thing to do, I think.



No? If the context is clear it is pretty common, e.g. prices, measurements.

Or do you say "Ich bin eins Komma acht fünf Meter groß."?


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## niku

In English, at least, the use of ‘forty-five’ would be utterly wrong. And there is logic behind this custom!

You can read 10,045 as
(a) Ten thousand(s) and forty-five, or
(b) One Zero Zero Four Five.

In the former, at soon as the first term has been said you know the magnitude of the number you are dealing with. (which is the most important thing about the number being quoted.) In the latter, you would first have to _store_ the whole phrase in your memory, then process it to _convert_ the phrase to the first form before you can make sense of it.

The situation with 0.10045 is the opposite. You can read it as:
(a) Point One Zero Zero Four Five, or
(b) Point ten thousand and forty-five.

In the former, as soon as the first term is said, you get an idea of the magnitude involved. So, as soon as you hear ‘One’ (or even better, ‘One Zero’), you can say, "Stop right there! I have no need of any more precision!". In the latter, you would have to listen to at least the first few terms, and then _convert_ the phrase into the former form to make sense of the number.

All this apart from what _Lingpil_ said, which also is an important point.

@Frank78: Perhaps the "weaved form" is acceptable when quoting prices because we know beforehand (i) that the number will contain only a few significant digits (2, or at most 3), so nobody will get bored or angry, and (ii) that all the digits which are quoted will be _put to use_, so nobody will rue about having his time wasted. Neither of them are true in most other cases, and especially, in engineering contexts.


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## manfy

niku said:


> @Frank78: Perhaps the "weaved form" is acceptable when quoting prices because we know beforehand (i) that the number will contain only a few significant digits (2, or at most 3), so nobody will get bored or angry, and (ii) that all the digits which are quoted will be _put to use_, so nobody will rue about having his time wasted. Neither of them are true in most other cases, and especially, in engineering contexts.



True! Not only for prices but for 2 digit numbers in general. In German we have a tendency to read in 2 digit groups. (and I'm an engineer who works with numbers a lot - sometimes we tend to be obnoxiously precise and some other times we use whatever 'sounds better' !)

For example, 2.20 meters I may pronounce as "zwei Meter zwanzig" or "zwei Komma zwei Meter" (even though a purist mathematician might correct me with "zwei Komma zwei null Meter")
Also, 644.2518 I'd probably pronounce as "sechs vierundvierzig Komma fünfundzwanzig achtzehn" if I know that the other person is familiar with numbers, rather than the formally correct "sechs*hundert*vierundvierzig Komma zwo fünf eins acht" 
Or 2.200007 as "zwei Punkt zwei, viermal die Null, sieben"

What it boils down to is that speaker and listener must understand each other, no matter what format you use.


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## Glockenblume

Like often in German, you must distinguish between different variants of the language:
This time it's not formel versus informel but 
technical terms versus "normal" language.

As for the technical language of mathematics, we have learned at school:
1,359 > eins Komma drei fünf neun
4,20 m > vier Komma zwei null Meter

As for the technical language of ingenieurs or others, I don't know if it's the same or different.

As for "normal" language, a lot of of educated people say:
1,359 > eins Komma dreihundertneunundfünfzig (but you can also use the other solution)
4,20 m > vier Meter zwanzig

Attention if there are zeros after the comma:
In "normal" language,
"vier Euro fünf" is in general: 4,05 Euro
"ein Meter acht" is in general: 1,08 Meter
"ein Kilo fünfzig" is in general: 1,050 Kilo*

*also in "normal" language: "ein Komma null fünfzig Kilo"


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## Schimmelreiter

Glockenblume said:


> As for the technical language of mathematics, we have learned at school:
> [...]
> 4,20 m > vier Komma zwei null Meter


Why not _vier Komma zwei_​?


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## manfy

Schimmelreiter said:


> Why not _vier Komma zwei_​?


I think, that's just a common mathematical convention: when it's *written* 4.20 then you normally spell it out as "vier Komma zwei null" (possibly to clearly indicate the precision of the number given, in this case 2 digits after the comma)



Glockenblume said:


> "ein Kilo fünfzig" is in general: 1,050 Kilo



I agree with the rest but this statement is a definite no-no!! "Ein Kilo fünfzig" I'd always understand as 1.5kg, UNLESS the statement is a successor to other statements where always "x Kilo y Gramm"-format was used!


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## niku

Glockenblume said:


> As for "normal" language, a lot of of educated people say:
> 1,359 > eins Komma dreihundertneunundfünfzig (but you can also use the other solution)
> 4,20 m > vier Meter zwanzig
> 
> Attention if there are zeros after the comma:
> In "normal" language,
> "vier Euro fünf" is in general: 4,05 Euro
> "ein Meter acht" is in general: 1,08 Meter
> "ein Kilo fünfzig" is in general: 1,050 Kilo



If anyone finds it confusing (like I did!), and is looking for the logic behind this:
For Euros, the next smaller denomination is Cents.
For Meters, the next (common) smaller denomination is Centimeters.
For Kilometers, the next (common) smaller denomination is Meters.

So, essentially, 
"vier Euro fünf" = 4 Euros, 5 [Cents].
"ein Meter acht" = 1 Meter, 8 [Centimeters].
"ein Kilo fünfzig" = 1 Kilo, 50 [Grams].
"vier Meter zwanzig" = 4 Meter, 20 [Centimeters].

Edit: _manfy_ said something similar.


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## Glockenblume

manfy said:


> I agree with the rest but this statement is a definite no-no!! "Ein Kilo fünfzig" I'd always understand as 1.5kg, UNLESS the statement is a successor to other statements where always "x Kilo y Gramm"-format was used!


Ich glaube, hier liegen deutsch-österreichische Verständigungsprobleme vor (Ich hätte präzisieren müssen, dass es um den Sprachgebrauch in Deutschland geht - Entschuldigung ):
In Deutschland verwendet man keine "Dekas" wie in Österreich - daher ist das Kilogramm-Gramm-Format den meisten Sprechern klar ...


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## niku

Schimmelreiter said:


> Why not _vier Komma zwei_​?



An addition to _manfy_’s reply above: The _null_ is important because it tells us that the number being quoted is reliable upto the second digit after the decimal point.

_vier Komma zwei Meter_ would mean, roughly, that the number (e.g., the length of a part) could be anywhere from 4.1 to 4.3. (Because, for one, the measuring instruments we used could measure with no greater precision.)
Similarly, _vier Komma zwei null Meter_ would mean, that the number is anywhere between 4.19 to 4.21. 
As you can see, there is a huge difference between the two. Even though both the numbers are ‘4.2’, the latter ‘4.2’ is much more precise. So, for example, if this were the size of a part I were fitting in a machine, the part it would fit in would require a much greater tolerance in the former case.


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## Hutschi

Frank78 said:


> No? If the context is clear it is pretty common, e.g. prices, measurements.
> 
> Or do you say "Ich bin eins Komma acht fünf Meter groß."?


It is "Einmeterfünfundachzig".

1,10 - Mostly I'd say in daily life "Einskommazehn". This rule holds up to "Einskommaheunundneunzig"-1,99. 
There is the joke;
Was ist größer, Einskommaneun oder Einskommazehn.


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## Arukami

Frank78 said:


> No? If the context is clear it is pretty common, e.g. prices, measurements.
> 
> Or do you say "Ich bin eins Komma acht fünf Meter groß."?



You are right, of course. Without context, I just thought of reading the numbers on their own. 
I'd say, "Ich bin eins fünfundachtzig" in this case.


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## Frank78

Glockenblume said:


> Ich glaube, hier liegen deutsch-österreichische Verständigungsprobleme vor



Sicher nicht. Ein Kilo fünfzig ist immer 1,50 und nicht 1,050. Wie soll man auch sonst zwischen ,050 und ,50 unterscheiden?

Die zusammengesprochenen Zahlen nach dem Komma verwende ich nur bis zum Hunderstel, also maximal zwei Nachkommastellen.


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## Glockenblume

Frank78 said:


> Sicher nicht. Ein Kilo fünfzig ist immer 1,50 und nicht 1,050. Wie soll man auch sonst zwischen ,050 und ,50 unterscheiden?
> 
> Die zusammengesprochenen Zahlen nach dem Komma verwende ich nur bis zum Hunderstel, also maximal zwei Nachkommastellen.


Dann scheint es unterschiedliche Verwendungsweisen zu geben - das ist mir auch nicht bewusst gewesen  ...
Aber ich bin mir sicher, das schon so gehört zu haben, wie ich es beschrieben habe.

Also folglich präzisiert man in diesem Fall besser die Einheiten: 
Ein Kilo fünfzig Gramm


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## Hutschi

I want to extend a little bit and hope it is on topic.
How would you speak longer decimal, and how would you group them?

Example
3,567455566777445465

Would you speak the groups than as digits or as numbers?


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## Glockenblume

Hutschi said:


> I want to extend a little bit and hope it is on topic.
> How would you speak longer decimal, and how would you group them?
> 
> Example
> 3,567455566777445465
> 
> Would you speak the groups than as digits or as numbers?


In mathematics:
drei Komma fünf sechs sieben vier fünf usw.

In every day life:
not always in the same manner ...


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## lingpil

Hutschi said:


> I want to extend a little bit and hope it is on topic.
> How would you speak longer decimal, and how would you group them?
> 
> Example
> 3,567455566777445465
> 
> Would you speak the groups than as digits or as numbers?



To escape the question: I don't see any reason why I should *pronouce* all this digits. While speaking about such a number, I would stop at 3,567 rounding the rest. Such a precise indication can usually only be found in reports, which means in *written* form. In a presentation among scientists or engineers I would presentate the full number via powerpoint or in another written form.
To answer the question: If I'm actually supposed to pronounce it completely, I would do it digit by digit.


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## Glockenblume

lingpil said:


> To escape the question: I don't see any reason why I should *pronouce* all this digits. While speaking about such a number, I would stop at 3,567 rounding the rest. Such a precise indication can usually only be found in reports, which means in *written* form. In a presentation among scientists or engineers I would presentate the full number via powerpoint or in another written form.


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## djweaverbeaver

Schimmelreiter said:


> Originally Posted by *Glockenblume*
> 
> 
> As for the technical language of mathematics, we have learned at school:
> [...]
> 4,20 m > vier Komma zwei null Meter
> 
> 
> 
> Why not _vier Komma zwei_​?
Click to expand...


If significant figures are important, then I'm sure this is just as wrong in German as it is in English.


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## manfy

lingpil said:


> To escape the question: I don't see any reason why I should *pronouce* all this digits. While speaking about such a number, I would stop at 3,567 rounding the rest. Such a precise indication can usually only be found in reports, which means in *written* form. In a presentation among scientists or engineers I would presentate the full number via powerpoint or in another written form.
> To answer the question: If I'm actually supposed to pronounce it completely, I would do it digit by digit.



Fully agreed! In spoken language such ultra-long numbers, be it before or after the decimal point, have very rarely much meaning. Nobody can follow a speech and simultaneously recalculate a formula with ten digit precision in his mind.
I know there exist some people who can recite the number pi up to 10 or 20 digit precision - but for me it's still just "drei Komma vierzehn *und so weiter*"  And yet, I never had problems this way, not even with the most pedantic mathematicians. 
That precision and those details can be very very important, of course, but only on paper (or these days on computer) but practically never in spoken language.


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## Schimmelreiter

djweaverbeaver said:


> Schimmelreiter said:
> 
> 
> 
> 
> 
> Glockenblume said:
> 
> 
> 
> As for the technical language of mathematics, we have learned at school:
> [...]
> 4,20 m > vier Komma zwei null Meter
> 
> 
> 
> Why not _vier Komma zwei_​?
> 
> Click to expand...
> 
> If significant figures are important, then I'm sure this is just as wrong in German as it is in English.
Click to expand...

I know of no mathematical convention that distinguishes between x = 4.2 and x = 4.20. If 4.2 were a rounded value, it would be x ≈ 4.2. But then, my knowledge is what I learnt very long ago.


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## djweaverbeaver

Schimmelreiter said:


> I know of no mathematical convention that distinguishes between x = 4.2 and x = 4.20. If 4.2 were a rounded value, it would be x ≈ 4.2. But then, my knowledge is what I learnt very long ago.



*Signifikante Stellen* und *Experimentielle Fehler* are *very important* in scientific calculations, especially since you don't want to appear more accurate than the equipment you are using is capable of determining.  I've gotten enough points taken off on exams and lab reports to know this.


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## niku

Schimmelreiter said:


> I know of no mathematical convention that distinguishes between x = 4.2 and x = 4.20. If 4.2 were a rounded value, it would be x ≈ 4.2. ...


All measurements give approximate results. In other words, all results of all measurements are rounded or truncated values.


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## Schimmelreiter

niku said:


> Schimmelreiter said:
> 
> 
> 
> I know of no mathematical convention that distinguishes between x = 4.2 and x = 4.20. If 4.2 were a rounded value, it would be x ≈ 4.2. ...
> 
> 
> 
> All measurements give approximate results. In other words, all results of all measurements are rounded or truncated values.
Click to expand...

In Christos's question, there's no mention of measurements:





Christos1 said:


> Ι would like to ask how can we read the "Dezimalzahlen"
> 
> For instance the numbers:
> 
> *1) 5,478
> 2) 34,9876*


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## niku

Schimmelreiter said:


> In Christos's question, there's no mention of measurements:



 I meant to say that almost all the numbers one may read in scientific literature are approximate, and the number of digits tells us the precision involved. Here, 0 is as good as any of the other nine numerals. So, if 0.011 is “Point Zero One One”, 0.010 is, by equal right, “Point Zero One Zero”.


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## manfy

Right! Bottom line: there is no real definitive binding standard written in stone for spelling out large numbers. Even in mathematics, science, engineering where the difference usually matters the speaker can choose his/her preferred style. Since the spoken word must always be backed up by written proof, I'd say, the chosen verbal format is not overly critical.

The usual format generally considered 'proper' for mathematical numbers: you read the integer portion as a single number and you spell out every single digit after the decimal point.
For measurements (time, weight, size,....) there's a much greater tendency to read these numbers in 2 digit groups or max. 3 digit groups, i.e.:

5,478 -> proper: "fünf Komma vier sieben acht" but also heard as: "fünf Komma vier achtundsiebzig" or "fünf Komma vierhundertachtundsiebzig"
34,9876 -> proper: "vierunddreißig Komma neun acht sieben sechs" but also heard as: "vierunddreißig Komma achtundneunzig sechsundsiebzig"

This is only valid for spoken language! In writing you never spell out these numbers. The only notable exception is monetary values on Cheques and invoices, etc. There you use proper format for integer portion and 2-digit format for Cents.
In my country that's: $250.22 = "Two Hundred Fifty and Cents Twentytwo Only"
I'm not too sure about the recommended German format for that (...seit's den Schilling nimmer gibt, kenn ich mich gar nix mehr aus...  )


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## stormwatch

Well, seen from outside (the German speaking areas), the thing is quite simple (and logical, foremost): *you read them how you write them*, that's how your brain is making the connection.

Grouping the digits by two makes it easier to remember, that's how a langauge should work, anything other makes it more (and unnecesarily) difficult. For example, what's the logic to reading the tens backwards, in German ? I know it's not proper to ask such questions (because the answer could be „_There's no logic, it is how it is, and that's it_”) but I cannot help it.


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## djweaverbeaver

stormwatch said:


> Well, seen from outside (the German speaking areas), the thing is quite simple (and logical, foremost): *you read them how you write them*, that's how your brain is making the connection.
> 
> Grouping the digits by two makes it easier to remember, that's how a langauge should work, anything other makes it more (and unnecesarily) difficult. For example, what's the logic to reading the tens backwards, in German ? I know it's not proper to ask such questions (because the answer could be „_There's no logic, it is how it is, and that's it_”) but I cannot help it.



< ... > First off, we don't read numbers two digits at a time after the decimal in English.  That may be how it's done in Romanian as they also do in French, but this is not standard in English.  We actually say out every number.  Furthermore, we only really read numbers how we write them when we actually spell out the numbers in words.

Lastly, it's beside the point to talk about which language is more logical than another.  It is completely logical, at least to the extent that it doesn't cause confusion, for those who speak the language, which is the only thing that matters.  In that case, I could question why you would read the numbers two at a time when you might end up with an odd set of numbers. Let us refrain from making such statements.


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## Christos1

and how can we read numbers such as 3, 456456456456.... (Repeating decimal)


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## Hutschi

Christos1 said:


> and how can we read numbers such as 3, 456456456456.... (*Repeating decimal)*



It is Drei Komma Periode  Vier Fünf Sechs as far as I remember.


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## stormwatch

djweaverbeaver said:


> < ... > First  off, we don't read numbers two digits at a time after the decimal in  English.  That may be how it's done in Romanian as they also do in  French, but this is not standard in English.  We actually say out every  number.  Furthermore, we only really read numbers how we write them when  we actually spell out the numbers in words.


Actually, I took that grouping thing from English because it is (seems)  more logical than, say, Romanian, where we don't use it, except for when  we tell very long numbers, like telephone numbers, or the Personal  Identification Code (13 digits long). But in English, anything bigger  than 109 and lesser than 9999 is told in grouping (the digits) by two.  And even bigger numbers than that are told by two (ex. 10-5-25 when it  is about the price of a car, would probably mean 10525 more than  anything else)

Even the decimals are told by grouping the digits  by two, unless it's a precision thing. In everyday life units are  subdivided and told in hundreds (not tens, not thousands). See the  currency, weights and measurements (in metric) etc. I bet you say you measure five feet eleven, not five feet one one.


djweaverbeaver said:


> Lastly, it's beside the point to talk about which language is more  logical than another.  It is completely logical, at least to the extent  that it doesn't cause confusion, for those who speak the language, which  is the only thing that matters.  In that case, I could question why you  would read the numbers two at a time when you might end up with an odd  set of numbers. Let us refrain from making such statements.


 I was not implying that some languages are more logical than others. Any  language has particularities that (may) seem ilogical to others, that  didn't grow up with it. But it's not beside the point to ask questions and  expecting to get logical answers, because history and tradition doesn't  cut it some times.

You should be able to ask why do we drive on the right side of the road (yes, in Romania too)  when in walking, as right-handed, as the majority of humans are, when  you cross paths with someone coming from the opposite direction, you  tend to go around each other by each-other's right, in order to shake  hand with him, or take your hat off in his direction, or just to put  yourself between him and the one you're with. The same rule applied to  the horseback riders and carriage drivers, ...until along came Napoleon and changed it, just to enforce his will in the Europe he conquered, and to spite the English. Is that a logical explanation, or just a ....historical one ?

I agree though, that this was grossly off-topic.


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## niku

@stormwatch, you are not in disagreement with djweaverbeaver. You are talking about digits occurring before the decimal point, while djweaverbeaver talked about digits occuring after the decimal point.
5'11" = 5.92'
In English, _Five Feet, Eleven Inches_ and _Five Point Nine Two Feet_.
Similarly, 5'11.50" = _Five Feet, Eleven Point Five Zero Inches._

 By the way, interesting information about the driving conventions!


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## djweaverbeaver

Hutschi said:


> It is Drei Komma Periode  Vier Fünf Sechs as far as I remember.



  But that would just be 3,456 not 3,456456456456... .  In English, we would say "*three point four five six repeating*".


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## Glockenblume

djweaverbeaver said:


> But that would just be 3,456 not 3,456456456456... .  In English, we would say "*three point four five six repeating*".


No, Hutschi is right.
You say "Periode" before the numbers to repeat endlessly.

Other example:
1,5333333333.... > "eins Komma fünf Periode drei"


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## djweaverbeaver

Glockenblume said:


> No, Hutschi is right.
> You say "Periode" before the numbers to repeat endlessly.
> 
> Other example:
> 1,5333333333.... > "eins Komma fünf Periode drei"



  Roger that! Thanks for the clarification.  I definitely missed the "Periode" until you pointed it out to me.


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