or Why you need to read Le Système international d’unités (8e édition)
How do you write very large or very small numbers? How, for example, would you write the speed of light out in full?
If you would write c = 299,792,458 m/s then please stop, because you’re doing it wrong. You can argue all you want about tradition, and “the way things have always been done” but you are still totally, absolutely, unequivocally wrong. There is a right way, an official, standardised way, to write very large and very small numbers, and it’s not with commas in them.
“Following the 9th CGPM (1948, Resolution 7) and the 22nd CGPM (2003, Resolution 10), for numbers with many digits the digits may be divided into groups of three by a thin space, in order to facilitate reading. Neither dots nor commas are inserted in the spaces between groups of three.”
The correct way to write the speed of light is c = 299 792 458 m/s. Ideally you’d use a special Unicode character, known as “NARROW NO-BREAK SPACE (U+202F)”, which stops text from wrapping around half-way through a number, but this isn’t very well supported, so the better-supported “THIN SPACE (U+2009)” or even just a normal space will do.
The reason for this is that the decimal point isn’t always a decimal point. Only 60% of countries use a full stop, whereas other countries use other marks. For example, a number that would traditionally be written in the UK as 123,456,789.01 would be written in France, Germany, Spain and many other countries as 123.456.789,01 and in Canada as either, depending on whether you’re working in English or French. This confusion (see this for example) was deemed undesirable and as such the scientific community declared in 2003 that:
The 22nd General Conference [of the BIPM],
considering that a principal purpose of the International System of Units is to enable values of quantities to be expressed in a manner that can be readily understood throughout the world …
reaffirms that “Numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups”, as stated in Resolution 7 of the 9th CGPM, 1948.
Remember that thousand separators are also used when dealing with very small numbers. I’ve provided some examples below if you’re struggling to get your head around them.
| Incorrect | Correct | Incorrect | Correct |
| 123 | 123 | 0.123 | 0.123 |
| 1234 | 1234 | 0.1234 | 0.1234 |
| 12,345 | 12 345 | 0.12345 | 0.123 45 |
| 123,456 | 123 456 | 0.123456 | 0.123 456 |
| 1,234,567 | 1 234 567 | 0.1234567 | 0.123 456 7 |
| 12,345,678 | 12 345 678 | 0.12345678 | 0.123 456 78 |
The first number in each column is both correct and incorrect … :)
In my experience what you are saying vis commas has caused countless students to fail to identify correctly orders of magnitude in larger numbers. I have stopped teaching what you preach because of this and have found that levels of understanding have increased dramatically. Personally I wish whoever thought this was a good system to teach had never been recognised. My priority is for my students and their understanding as opposed to convention.
Graham, you’re obviously teaching it wrong.
Graham, are you saying that the use of commas makes it easier for students to understand
Using commas to divide 1,000s and decimal points for “less than a whole” makes it clearer and quicker to correctly read any number. I live in an area where commas are used rather than decimal points – its horrible. A simple error when prescribing medication for example could be fatal. Put the commas in to break up 1,000s and decimal points in correctly and there can be no misunderstanding.
But the people who use “commas … rather than decimal points” probably think your system is horrible. Better to stick to spaces as thousand separators then everyone can use the same system.
when you see 2 commas you are sure of a million. If none, that means you need to count digits in order to understand the scalar quantity.
You can count spaces too?
Unless Im going blind, the first 2 rows of your table have correct and incorrect as the same value. Am I missing something?
For comparison only.
I find it far less readable with a space as opposed to a comma. I think the change is idiotic but it is what it is. No different than many other idiotic changes that have been pushed on us over the recent years.
Maybe the rest of the world should learn to adopt our way of writing numbers. Writing numbers with spaces e.g. 234 245 not 234,245 makes it look like there are two different numbers.
This is nonsense. If I ask you what a car weighed, and you wrote down 12 345 N, why would I think think you had written two weights? Your argument in nonsensical.
The logic of this, that the world uses commas and points differently, does not lead to the solution proposed. The parts of the world that don’t use commas as separators (for which you argue for spaces) instead use commas for the decimal. Thus, they would write – 0,1234 – so the use of spaces hardly makes things universal.
I simply would write the speed of light as 299792458 m/s without any break at all. Any spaces at all should technically be unnecessary.
Yes it does.
Technically, sure.
I expect that a third deliminator was introduced because other countries would prefer to maintain their own commonly used deliminator and wouldn’t be able to come to an agreement.
I’m curious though, why is the second number in each column not separated into “groups of three”?
With the second number, with four digits, this is not usually separated.
I agree with Steve! He has the right idea!
The standard says that ‘Numbers MAY be divided in groups of three…’. Therefore 299792458 and 299 792 458 are equally correct.
First, I’m not a numberphile (shout out to Numberphile YouTube) or an expert on this at all. Second, I may need to research more, but wouldn’t 299,792,458 m/s be faster to read than 299792458 m/s would be? Because what if the number was 2994758345215243? It would take a lot longer to read out what number I just typed. And yes, using spaces it would make it faster just like using commas. On a computer, until they incorporate a Uni-code break space or thin space key on to the keyboard, it would be tough to get me to try switching from a comma. I do like the idea of using spaces, and maybe I skipped a part of this article that might answer this, but what about for handwriting? “Who writes out checks anymore or handwrites anything?” says my 13 year old self. If you can’t read the amount they put in the box because they didn’t space the numbers out even, then you’d read what numbers they spelled out obviously. But still… even hand written notes with amounts would be hard to read. I even have a hard time spacing letters evenly in some words 10% of the time. I’m not yet for or against the use of commas or spaces, just wanted to get some opinions! Awesome website and article.
We use LaTeX and siunitx which does it automatically.
None are incorrect, all just come from different teachings. Just because it doesn’t align with your preference does not mean it’s incorrect. That’s almost like telling everyone their language is incorrect and the whole world should speak English. I asked my buddy in NASA how they use thousands/decimal separators and he simply replied “we use all of them”.
Nope, sorry, Jason. I double-checked with my buddy from NASA and she said that commas are incorrect.
To assert that convention, and tradition with respect to punctuation are simply irrelevant once some organization has made, a pronouncement, is absurd. Languages and symbols, for communication are made, out of established, conventions. It is equally, absurd to claim, as one commenter does, that using no separators in a large, number is “technically” correct. The purpose, of punctuation is to guide the eye and mind in decoding what it is on the page. A separator is not too crucial when we’re talking about 1000. But long before we get to 100 000 000 000 000 000 000 000 000 000 000, yeah, the separators, are useful and important. What is the “technical” standard, being alluded to? The ancients did without spaces between words. Presumably, the text could be, decoded–eventually. So who needs, punctuation at all or any spaces between words, and, sentences? Maybe, it has something, to do with the facts that we need, all the help we can get and that life is short?
No, David. Commas are wrong and spaces are correct.
Commas should idiots
I agree. Commas should idiots!
So the Americans got the date format logically wrong (why pririoritise the month over the day?) and the French so obviously got the number format wrong (commas are for lists and full stops to separate). But both these countries are so up themselves and wont admit mistakes the English have to agree to a compromise for the sake of world standardisation. Since the “period” is the correct ISO way to separate the whole numbers from fractions, that was the right way from the start.
And yes, foreign doctors have killed patients in the UK because no body told them we use commas differently as they inject them with morphine.
In addition as this has been a standard for so long, why has not a single computer manufacturer bothered to add the short space to a keyboard even those with number pads? I would like to use it but I am not going ot type 123 [insert>symbol look for an unnamed little space, double click, exit] 123 [ then do all that again]. Loads of people handwrite including teachers on white boards and lots of kids (especially boys) have dyslexia or dispraxia. In hand writing it is plain silly to insist people use spaces. Clarity
Its for technical and scientific documents at the moment. One day maybe numbers may format automatically in Word or Excel if Bill Gates pulls his finger out of his A*se and stops worrying about world peace and malaria for a few minutes.
ky, ths cmmnt sctn s sht shw. nstd f sng cnstrctv crtcsm gnst ppl rgng thr pnts, y dcd t ttck thm. Lt’s gt bst f hr!
– “Grhm, y’r bvsly tchng t wrng.”
– “Bt th ppl wh s “cmms … rthr thn dcml pnts” prbbly thnk yr systm s hrrbl. Bttr t stck t spcs s thsnd sprtrs thn vryn cn s th sm systm.” ( lk th nsrnss n ths cmmnt. Th “Prbbly” gts m vry tm).
– “Np, srry, Jsn. dbl-chckd wth my bddy frm NS nd sh sd tht cmms r ncrrct.” (NS s n mrcn gncy. n mrc, hv bn tght t s dcmls s sprtrs fr nmbrs gng vr th thsnds plc).
– “N, Dvd. Cmms r wrng nd spcs r crrct.”
S, th cnclsn hv drwn s tht y, Mr. Rd, r fll f sht. Y thnk t shld b n wy, nd n wy nly. Y hv n rbttls gnst nyn wh rgs gnst ths. nd, nstd f cmng p wth cnstrctv crtcsm f thr vws, y smply tll thm thy r wrng. Y hv n plc t tll ppl wht t blv nd ntl y cm p wth wy t rg yr pnt crss t ppl, my cnclsn wll sty th sm.
Gdby.
Completely with Mr Reid.
This link is all you need:
https://www.nist.gov/pml/special-publication-330/sp-330-section-5#5.4.4
At 94 I can handle spaces (although there is the problem of deciding if it’s one number or several). Commas avoid this and help discerning hundreds, thousands, millions, etc. Perhaps we should blame inflation!
It’s very annoying to import figures into a program only to discover someone’s polluted them with punctuation marks.
There’s only one space where using spaces, instead of commas or periods, is acceptable: math calculations, only as a personal preference and only if doing so is considered acceptable in the culture where you’re writing your numbers down.
Everywhere else, you should learn which decimal separators are considered acceptable in the language of that place you are writing. Many non-English and non-European places use commas (ex: South Africa), and in many cases they even use them in very different ways (Indian numbering system). Most newspapers and written documents across North America use commas as decimal separators, for example, and you certainly can’t enter calculations into a spreadsheet using spaces as separators.
To deliberately use spaces instead of commas in those settings will only serve to make you look either like A) a luddite or B) a wilfully ignorant pedant who probably spends most dinner parties shouting their opinions loudly at anyone in a 10-foot radius.
Nope, sorry, Raf, you’re wrong.
MrReid, you should not put a comma before “because.” That is very old-fashioned. I know that I learned in school to put a comma before “because” just like I learned to separate the thousands with commas, but that was over fifty years ago!
Okay, Boomer.
Totally agree. Also, you should change your WordPress locale from “English (US)” to “English (UK)”, since it’s clear you use British English.
crrct r ncrrct, f wnt t wrt 10,200,134 BVSLY WTH CMMS, wll wrt t tht wy, dn’t gv sht wht Y thnk. Ths s hw w d t n mrc. Tk t r lv t. f th wrld ndrstnds t, wh TH HLL CRS whthr y thnk CMM S WRNG. T S DMN WLL SR T RD!
THIS IS AWESOME , I GIVE THANKS TO YOU . One Question , forgive me if this has been covered already; Q. Whats the deal with numbers like this “151,62” or “16,1” : The first one I see often in spreadsheet(s) in the money/amount column where it appears at first glance to be $151.62 at first glance, and it cannot be a number sequence (i don’t think) and the second one I see for example “16,1 GB Free Space” on memory card etc.
why can’t you use a comma
Read the article, ethan.
Gss wht, thr r hndrds f thr nstttns, ncldng ctl rthgrphy lws wh prscrb crtn wys t s thr rspctv lngg, ncldng hw t wrt nmbrs. Jst bcs y rbtrrly hppn t prfr th rcmmndtn f n sch nstttn vr thrs ds nt mk t “nqvclly” rght. n fct, th lw sys y r wrng.
Y r wrng.
In some places a comma can get smudged making the number hard to read like on machine parts, so they space the numbers by some arbitrary amount. Registration codes, social security numbers and other types of data have an arbitrary spacing specific to the intended use.
There are times when commas are more useful and when spacing is more useful. It depends on the application. One system for all is not a sound idea. Different problems require different solutions instead of a one-size fits-all.
Whether its dashes, commas, periods, 3 spaces, 4 spaces, or more, or none, the idea is to make the digits readable. It was not meant to make the number clearer to read. It was not changed to codify or streamline numbers. To claim it was is a misconception. This had nothing to do with nationality but rather necessity.
This is a confusing subject and it would be better to allow people the freedom to choose what solution they want to use instead of being told to change their work habits to conform to a nearsighted biased self proclaimed elitist groups demands for a globalized solution. The argument is based on aesthetics rather than intended use, as a result function suffers. It don’t work better in all situations they just like the way it looks or think it makes them look smarter.
Computer engineers claim spacing makes reading the numbers easier for them. That is what they collectively decided to adopt as their local system. But it does not make it right. I will always write one million dollars as $1,000,000. It is what people expect to see, anything else will confuse them. If I was programming them I would use whatever system was in place be it octal, hexadecimal and space every four digits.
If I was doing physics then I would use scientific notation to express the speed of light because that is the convention. I would only write it differently if I was targeting a younger audience and then would use commas for better reception. Using spacing for everything is harsh.
My logic can be questioned but the systems that came about were because of this whether logical or not. It served peoples needs and emotions so maybe logic has nothing to do with it. It worked and people were happy. Telling them to change puts undo hardship on them as now they are being limited in how they chose to express themselves in a way that is comfortable to them and their audience. It’s mean and I don’t think beneficial.
I came here because the font I am using Linux Libertine G spaces numbers like this:
“1.23456 789 999”. I was looking for a way to close the gap between 6 and 7 but can’t. I have read books published using this type of system and it looks bad and unprofessional having an arrant gap in a number like 8.31788 785.
Anonymous…no vowels…a legend! Mr. Reid created this article just to troll any commenters…lol!
I am fully team spaces, no commas!
Since we are all getting very opinionated about this, here I go too.
I was in grade school in the seventies in Canada when the metric system came in, One day there was a new rule. Okay kids, no more commas, just spaces. It’s metric, it’s science! I was thrilled that scientists were using this and now I was too and I was just a kid.
I am home schooling my kiddo now and he was wholly confused with commas and decimals. I was shocked that he learned to use commas in the first place. What, are they going backwards 45 years in the math curriculum now? We received a new math textbook, and it thankfully advised with doing away with the comma because we are in Canada and metric. It did acknowledge other countries may do it differently.
The confusion for my son had to do with the crossing of commas and periods into math. For him, this was only punctuation. A comma meant pause, but still a continuation of a number.
The decimal, to him a period, meant stop and a new number begins, not a fraction of a number. So, the comma works much the same in math but not a period/decimal. Stupid school, no consistency! A lot of repeating and explaining of concepts later and the light bulb went on.
Commas in math make my eyes roll. You don’t really need either. If you don’t know what a four digit or more number reads without commas or spaces you need to expose yourself to numbers more.
People who need commas in numbers are probably the same type of people who think you need to know the definition of a transitive verb or a dangling participle to write a sentence. You know the type, they’re a bit extra.
Also, I am team “no dashes in phone numbers.”
Could the numbers written in this article be adjusted to have spaces, please? http://wordpress.mrreid.org/2015/10/21/one-million-hats/
“For each person, there is only a one-in-a-million chance that they have picked their own hat, and thus a 999999 in 1000000 chance that they have not got their own hat.”