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Why do we put a comma after three digits when using big numbers?

  1. Sep 24, 2010 #1
    Why is it that commas(or decimals) are used to group sets of 3 digits together? Like for a million you usually see;

    1,000,000

    Why don't we group digits together in groups 4;

    100,0000

    Or since we use a base 10 numbering system, why not 5 or 10;

    10,00000 or 1,0000000000

    Is there something magical about the number 3 or is it just used because its easy to count? Why we're on the topic, why do we say 1 million is 1,000,000? Why isn't 1 million 1,000,0000?

    If you haven't figure it out yet, I'm procrastinating from doing my homework.
     
  2. jcsd
  3. Sep 24, 2010 #2

    Supposedly, it makes it easier to read. Also you'll note that we don't do it to the right of the decimal; we simply leave extra spaces between the groups of three...

    1, 000, 000, 000 . 000 000 000 000



    Probably just arbitrarily decided. Could be the perceived mystique of the number three--as in Religion and Big Business--and as you mention also later.



    I'm with you on that: for the sheer familiarity of the numbers; and relative easy with which they are used (because we have fingers as such, incremented in sets of 5). But that IS obviously more difficult to see, bunched up like so.



    There is a sort of nomenclature to it after a point; I'm sure you know. Milli implies a thousand; so a million is a thousand thousands. And after that, the roots take on a more predictable form: Billion--as in the 2nd set after a Million--like a bicycle has 2 wheels; Trillion--as in the 3rd set after a Million--like a tricycle has three wheels; Quadrillion; Quintillion.

    But I'm not sure after that. I would assume the root would be something to do with six (like hexa- or sexa-).

    Also, I re call reading somewhere, that a Billion and a Trillion are actually switched in British culture (meaning our Billion is really their Trillion; and our Trillion is really their Billion).


    Do your damn homework Toph. :biggrin:
     
  4. Sep 24, 2010 #3

    BobG

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    We could have chosen to group by 4, but not by 5, and definitely not by 10.

    Humans have an innate ability to recognize how many are in small groups (4 or less) - even if they don't have a word for those amounts. In other words, humans can subitize up to 4 objects. Once you get to 5 or 6, the only way to figure out how many objects are in a group is by counting. (I don't necessarily believe that 4 is the upper limit for subitizing. It may be 5. Or, perhaps the ability to subitize 5 is something that's developed by experience, not an innate ability).

    The reason is that humans don't naturally think of numbers linearly. They think of numbers logarithmically. An infant can realize the difference between 8 objects and 16 objects. They can recognize the difference between 1 object and 2 objects. They can't recognize the difference between 8 objects and 9 objects. The ratio of 9 to 8 is just too close to being 1.

    Humans usually don't start thinking of numbers linearly until around 3.5 years of age. It depends on how persistently and frequently the adults around them indoctrinate them into converting to linear thinking about numbers. You sing counting songs over and over, every day of your life, you eventually give up and start believing the songs.

    In civilizations that don't count, the transition never takes place. Ask an American how many objects would make a group halfway between 9 an 1 and they'll form a group of 5. Ask someone that never learned how to count, and they'll form a group of 3.

    I guess, by habit, humans could learn that numbers are grouped by 5, but it's something they'd have to be trained by repetition to recognize. Grouping by 5 isn't something they'd inherently recognize.

    Here's an interesting piece from Radio Lab about the subject: Innate Numbers. (It also explains how they figure out whether an infant can recognize the difference in numbers or not).
     
    Last edited: Sep 24, 2010
  5. Sep 24, 2010 #4
    Interesting. Let's do a poll. Which is better to read?

    1000000

    1,0,0,0,0,0,0,0

    10,00,00,00,00,00

    100,000,000,000

    1000,0000,0000,0000

    10000,00000,00000,00000

    100000,000000,000000,000000

    1000000,0000000,0000000,0000000
     
  6. Sep 24, 2010 #5
    The traditional Chinese method uses groups of 4, although the system is not directly comparable to the Arabic one we use.
     
  7. Sep 24, 2010 #6
    No fair, we're all used to a particular system.
     
  8. Sep 24, 2010 #7

    BobG

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    That's exactly what I was thinking until I looked at the numbers. Grouping by 4 would be perfectly acceptable, as well. Grouping by 2 is just too many groups. Each group is easy to read, but now you have a lot of groups to count (four groups of 3, four groups of 4, or 6 groups of 2).

    The bigger flaw is using numbers with a different number of digits.
     
  9. Sep 24, 2010 #8

    Pythagorean

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    They allow you identify the powers of 10^3:

    kilo
    mega
    giga

    etc.
     
  10. Sep 24, 2010 #9
    The traditional Chinese system allows you to identify the powers of 10^4.
     
  11. Sep 24, 2010 #10

    Pythagorean

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    In my short history on Earth, I've only encountered names for power of 10^3 in the sciences.

    (and 10^-2, centi, being the one exception I can think of)
     
  12. Sep 24, 2010 #11

    BobG

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    So, you're basically saying you grew up in a Western culture and, therefore, studied science using a Western language.
     
  13. Sep 24, 2010 #12
    That's true to some degree, but if you look at the distribution of groupings, there seems to be an island of stability between 3 and 4 groupings, and anything below or above is just too cumbersome to the eye.
     
  14. Sep 24, 2010 #13
    To be sure, there are Chinese with limited experience as well. I think the Chinese names are:
    10^4 - wan
    10^8 - i
    10^12 - zhao

    I'm more familiar with the Japanese names:
    10^4 - man
    10^8 - oku
    10^12 - cho
     
  15. Sep 24, 2010 #14
    Also, large numbers are rarely displayed in full length length. They are either displayed in scientific notation with the first few significant digits followed by an index: mega, giga etc.

    The largest number you would handle in real life could be up to a million, and it divides nicely in 3 groupings: 1,000,000

    but that's it I guess. Nobody will give you a 10^19 to write on paper in full.
     
  16. Sep 24, 2010 #15
    Our marketing team always wanted 3 letter acronyms for the all our product names.
     
  17. Sep 24, 2010 #16

    Pythagorean

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    It's my assumption that's the frame in which the question was... well, framed.
     
  18. Sep 24, 2010 #17
    The Ramans do everything in threes.

    Arthur C Clarke
     
  19. Sep 24, 2010 #18

    BobG

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    The Air Force likes 3 letter acronyms. They even make up 3 letter acronyms that they haven't determined a meaning for yet. Check out TBD in any Air Force glossary. It's just followed by "to be determined". Nearly 30 years and I'm still filled with anticipation of the day....
     
  20. Sep 24, 2010 #19
    But in scientific writing, the commas aren't used at all.
     
  21. Sep 24, 2010 #20




    Adjusted slightly, for comparison sake...


    (A) 1000000000000000000000000000 (NO COMMAS)


    (B) 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 (COMMAS AFTER EVERY DIGIT)


    (C) 10,00,00,00,00,00,00,00,00,00,00,00,00,00 (GROUPS OF 2)


    (D) 1,000,000,000,000,000,000,000,000,000 (GROUPS OF 3)


    (E) 1000,0000,0000,0000,0000,0000,0000 (GROUPS OF 4)


    (F) 100,00000,00000,00000,00000,00000 (GROUPS OF 5)


    (G) 1000,000000,000000,000000,000000 (GROUPS OF 6)
     
  22. Sep 24, 2010 #21

    BobG

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    All of those numbers are way too big. I could live with:

    1,000,000,000,000,000 Terraunits

    or

    1000,0000,0000,0000 Zhaounits

    but I think I'd prefer the Zhaounits.

    Then again, if I used numbers that big on a routine basis, I'd probably learn what came after terra-; maybe even what came after zhao-.
     
  23. Sep 24, 2010 #22
    Bad example, numbers that large are never written in comma notation. It's always either in scientific notation or spelled out, ie. "one thousand trillion trillion."
     
  24. Sep 26, 2010 #23
    It isn't illegal. It's just impractical.
     
  25. Sep 26, 2010 #24

    cristo

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    That's not true. In British a billion is a million million, and a trillion is a million billion. Of course, noone really uses these anymore, but instead uses the American terms.
     
  26. Sep 26, 2010 #25
    You were right...


    http://dictionary.reference.com/browse/billion

    "1, 000, 000, 000 --> American Billion (1 followed by 9 zeroes)."

    "1, 000, 000, 000, 000 --> British Billion (1 followed by 12 zeroes)."




    http://dictionary.reference.com/browse/trillion

    "1, 000, 000, 000, 000 --> American Trillion (1 followed by 12 zeroes)."

    "1, 000, 000, 000, 000, 000, 000--> British Trillion (1 followed by 18 zeroes)."



    Plural of 0...
    http://dictionary.reference.com/browse/zeros

    ...I prefer the -es alternative.
     
    Last edited by a moderator: Sep 26, 2010
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