Stop Putting Commas In Your Numbers

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

27 thoughts on “Stop Putting Commas In Your Numbers

  1. The first number in each column is both correct and incorrect … :)

  2. 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.

  3. Graham, are you saying that the use of commas makes it easier for students to understand

  4. 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.

  5. 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.

  6. 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.

  7. Unless Im going blind, the first 2 rows of your table have correct and incorrect as the same value. Am I missing something?

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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”?

  14. 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.

  15. 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”.

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