# Formatting numbers in a book about mathematics

Would anyone be kind enough to point me to a reliable source (preferably on line) where I can find definitive answers to how to format numbers consistently within a book about maths aimed at popular readers.

In particular, the use of thousand dividers (UK/US style commas)

Dates, eg, 'written in 1992' don't have them.

Long numbers, eg '10,000,001' seem clearer with them in text, but then you get lines that include things like '3141/1000'. Should this be as just typed, or '3,141/1,000'?

Examples of other things I should look out for would be very welcome. Thanks

• Wikipedia has some useful information. I tend to use spaces between the 3-digit stanzas. 3141/1000 is far clearer, though I'd use a horizontal bar if possible. 314 159/100 000 needs one. – Edwin Ashworth Feb 27 '14 at 9:35
• I would leave out the dividing commas for numbers less than 10,000 and put it in for numbers larger. This is fairly standard practice, and certainly suitable for a popular book. – Peter Shor Feb 27 '14 at 15:34

One Megabyte = .000,976,6 Gigabytes How to write numbers and their digits universally

A - Current official rules leave some choices

NIST, Wikipedia and other authorities (official or not) apparently concur to recommend or impose to group the digits by 3 starting from the (single) "decimal separator", the groups of 3 digits being separated with "thousand separators", with dropping that (then unique) thousand separator when the number of digits left or right from the decimal separator is 4.

The choice of the particular DEC and THND separators is left to actual popular use, which depends on the language.

For a long time that actual popular choice for DEC and THND separators was "DOT and COMA" in English (US, UK, etc), and the reverse ("COMA and DOT") in French:

• The speed of light in a vacuum is 299,792.46 kilometers per second
• La vitesse de la lumière dans le vide est 299.792,46 kilomètres par seconde

In the recent decades that has changed in French, and even in English, to "DOT and SPACE" (the fictive example below is built after Wikipedia Speed of light and Vitesse de la lumière):

• The speed of light in a vacuum is 299 792.46 kilometers per second
• La vitesse de la lumière dans le vide est 299 792,46 kilomètres par seconde

B - Applying those rules and choices

B1. The old rules ("DOT and COMA" and "COMA and DOT") had the bad effect of ambiguity when reading in another language. The new tacit rule (THND represented with an NBSP) succeeds in removing that ambiguity with minimum hurt to national habits, yet introduces a side hurt to the accuracy or reliability of the writing: the NBSP inevitably gets too often replaced with a visually indistinguishable ordinary space, making the number line-broken hence too often wrongly read, no matter the reader being an human or a program.

B2. English, French and other languages, aside from all their contradictions, at least concur, in ordinary literal writing, on using DOT to separate sentences and COMA to separate sub-sentences; so in a phrase (or sentence) you can have several comas, but ONE dot. Unifying that principle to numbers, and trying to make it as simple, clear, universal, as possible, leads logically and naturally to represent DEC with DOT and THND with COMA; so in this case (oppositely to Unit Systems), IMO the French (and others) should have simply switched to the English way: ONE DOT at the end of the phrase (or number), SEVERAL COMAS between sub-phrases (or 3-digit groups).

B3. The above should apply IMO same way before and after the DEC (decimal separator)

B4. When there are no digit before the DEC, official rules recommend or impose to put a leading zero. I would oppositely drop it, or at least make it optional; for instance in a long vertical column, the visual length of the numbers would remain, one more digit to the right, a correct representation of the order of magnitude of the involved number; accessorily the one-char saving is sometimes useful (e.g. in some large tables).

B5. Finally the choices I would recommend, as compliant as possible to official rules, simple to write, easy to read and friendly to anyone on the planet, looks as shown in this example:

• One Megabyte = .000,000,953,674,316,406,2 Terabytes = .000,976,562,5 Gigabytes = 1 Megabyte = 1024 Kilobytes = 1,048,576.00 Bytes

Versailles, Thu 27 Feb 2014 22:28:20 +0100, edited (formatting) 22:42:40

• Michel, thank you for a well-reasoned explanation. One question remains - in the context, it's clear that 1024 Kilobytes refers to those units, while 1024 AD to a year. Since these involve a thousand + units, shouldn't they logically have commas after the 1 for consistency? I suspect we will never see commas in dates, but in other forms of unit references, why not? – Leon Conrad Feb 28 '14 at 8:09
• Leon Conrad 28 Feb 2014 08:09:48 GMT, the choices I made (and recommend) are trying to be as clear, simple, immediately and unambiguously understood by anyone on the planet; as such they try to add NO particularities for some sorts of numbers, like time or else. This is why "1024", having exactly 4 digits next to the (implied) DEC (decimal separator), omits the THND (thousand separator), no matter if describing a time or any other quantity. Thanks anyway for your kind reply (and from the start for an useful question IMO). Versailles, Fri 28 Feb 2014 16:12:00 +0100 – Michel Merlin Feb 28 '14 at 15:12
• Understood. Merci beaucoup! – Leon Conrad Feb 28 '14 at 15:18

I suggest, rather than Wikipedia, you download a copy of the NIST or ISO standards document.

• Fascinating document, thank you, but as far as I can make out internally inconsistent, eg in 2.1.1.5, there's a reference to '1H, 0.000 379 9 mole' with spaces after a decimal point, which I've never seen before; in 3.1, top of p 30' '5000 μs−1 = 5000 (μs)−1' with no space after the 5. All references seem to be to numbers of units, rather than numbers per se. I'm back to square 1! – Leon Conrad Feb 27 '14 at 15:26
• @Leon: yes, spaces in groups of 3 to the right of the decimal point is correct. There's no space in "5000" because the number is "too small." Not enough digits to warrant any spacing -- same as if you were using commas. – Carl Witthoft Feb 27 '14 at 15:40
• +1 This is very much the correct document for formatting numbers and SI units. See section 5.3.4. Numbers of more than four digits either side of the decimal marker are to be separated into groups of three using a space. Please do not use Wikipedia as the definitive guide for something like this. – long Feb 27 '14 at 21:48

I suggest you use the same rules as Wikipedia suggest to their editors for numbers and dates.

http://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style_(dates_and_numbers)

• Any advance on this passage from there: 'Note that the variety of English does not uniquely determine the method of numbering in an article. Other considerations, such as conventions used in mathematics, science and engineering, may also apply, and the choice and order of formats and conversions is a matter of editorial discretion and consensus.),? – Leon Conrad Feb 27 '14 at 12:03