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

8 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.

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