In English (I think this is universal anyway) we use the 1s, 10s, and 100s in a cycle. One, one thousand, one million; twenty two, twenty two thousand, twenty two million; one hundred and forty six, one hundred and forty six thousand, one hundred and forty six million, etc.

Who decided to cycle every (3x+1)th digit?

  • $\begingroup$ Note that SI inherited the tradition of incrementing by a thousand (mega-, giga-, tera-, peta-, etc.). $\endgroup$ Nov 24 '10 at 15:33
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    $\begingroup$ This would be more suitable on english.stackexchange.com . (BTW, "I think this is universal anyway" --> no, China and Japan cycles every (4x+1)th digit, and India every (2x+4)th...) $\endgroup$
    – kennytm
    Nov 24 '10 at 15:35
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    $\begingroup$ I think that this has as much right to be here as any question as to the definition of "primes" to exclude 1 or the "naturals" to include 0. It may be a linguistic convention, but it is a linguistic convention about describing mathematical objects. And keep in mind that the analogous development for counting in the antiquity needed no less a personage than Archimedes to propose it for the record! $\endgroup$ Nov 24 '10 at 16:02
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    $\begingroup$ I see one vote to close; I'm casting a virtual vote against closing due to the same reasons Niel mentioned. $\endgroup$ Nov 24 '10 at 16:10
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    $\begingroup$ I disagree with Niel and J.M., but regardless of the appropriateness of the question here, it seems to me that the answer would have to come from knowledge of the historical usage of number names in common language, not specifically in mathematical texts, so you would get a better answer at a linguistics forum. $\endgroup$
    – user856
    Nov 24 '10 at 16:39

This is not universal. In Spanish, for example, you need a thousand thousands to get a million. And "billion" is not, as in the United States, a thousand million; no, "billion" means "a million millions"; then trillion means "a billion billions"; quatrillions are "a trillion trillion", etc.

  • $\begingroup$ So does in Portugal. This subject is important in the EU, when translating documents from different languages. In this Bulletin ec.europa.eu/translation/bulletins/folha/folha18.pdf (page 14) the Portuguese Translation General Director of the European Commission explains the correct translation of "billion". In 1948 the 9th. General Conference on Weights and Measures recommended the use of the «6N rule». $\endgroup$ Nov 24 '10 at 20:28

Warning: I am not a linguist, so my answer is to be taken as an educated guess, no more.

It is essentially historical and the development of this system is told at http://en.wikipedia.org/wiki/Long_and_short_scales . As said above, it is not universal, even in other base-10 languages : East Asia and India have different systems. Even in western scientific tradition, Archimedes used a myriad (10⁴) based system for big numbers and French use the long scale, a 10⁶ based system. The choice of a system grouping the digits by 3 is therefore an historical accident, and we could as well have ended with a different grouping.

However, the need of very large number seems to only exists for some technical use (science, accounting, religion) and do not emerge naturally in the language evolution. Therefore, the systems for big numbers are constructed by the specialist in question and do not blend well with the other numeral. In French, for example, the word "mille" (thousand) is grammatically a number (a cardinal numeral) but "million" is a simple noun. Hence the "need" for a "restart". I guess it's similar for other languages.


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