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

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Discussion Overview

The discussion revolves around the use of commas to group digits in large numbers, specifically why groups of three are commonly used instead of other group sizes like four or five. Participants explore the implications of this grouping in terms of readability, cultural practices, and cognitive recognition of numbers.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants suggest that grouping by three makes numbers easier to read and is a convention that has been adopted, while others speculate it may be arbitrary or culturally influenced.
  • One participant mentions that humans have an innate ability to recognize small groups of objects, typically up to four, which may influence the preference for grouping by three.
  • Another viewpoint is that the traditional Chinese numbering system uses groups of four, indicating cultural variations in digit grouping.
  • Some participants propose that the familiarity of the base 10 system and the structure of large number names (million, billion, etc.) contribute to the preference for grouping by three.
  • A poll is suggested to compare readability of different grouping systems, highlighting that familiarity with a particular system may bias perceptions of readability.
  • There are mentions of scientific notation and the practicality of using abbreviated forms for very large numbers, which may not require full-length representations.
  • Several participants note that the use of three is prevalent in various contexts, including marketing and military acronyms, suggesting a broader cultural tendency towards triadic structures.

Areas of Agreement / Disagreement

Participants express a range of views on the reasons for grouping digits in threes, with no clear consensus on whether this practice is inherently better or simply a matter of convention. The discussion includes competing perspectives on cognitive recognition and cultural practices.

Contextual Notes

Some claims about cognitive recognition of numbers and cultural practices are based on assumptions that may not be universally applicable. The discussion does not resolve the question of why specific group sizes are preferred.

Topher925
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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.
 
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Topher925 said:
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


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


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

100,0000


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.


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

10,00000 or 1,0000000000


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.


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


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).


If you haven't figure it out yet, I'm procrastinating from doing my homework.

Do your damn homework Toph. :biggrin:
 
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).
 
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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
 
Topher925 said:
Why don't we group digits together in groups 4
The traditional Chinese method uses groups of 4, although the system is not directly comparable to the Arabic one we use.
 
what said:
Which is better to read?
No fair, we're all used to a particular system.
 
what said:
Interesting. Let's do a poll. Which is better to read?

100,000,000,000

1000,0000,0000,0000

Jimmy Snyder said:
No fair, we're all used to a particular system.

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.
 
They allow you identify the powers of 10^3:

kilo
mega
giga

etc.
 
Pythagorean said:
They allow you identify the powers of 10^3:

kilo
mega
giga

etc.
The traditional Chinese system allows you to identify the powers of 10^4.
 
  • #10
Jimmy Snyder said:
The traditional Chinese system allows you to identify the powers of 10^4.

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)
 
  • #11
Pythagorean said:
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)

So, you're basically saying you grew up in a Western culture and, therefore, studied science using a Western language.
 
  • #12
Jimmy Snyder said:
No fair, we're all used to a particular system.

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.
 
  • #13
Pythagorean said:
In my short history on Earth, I've only encountered names for power of 10^3 in the sciences.
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
 
  • #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.
 
  • #15
Our marketing team always wanted 3 letter acronyms for the all our product names.
 
  • #16
BobG said:
So, you're basically saying you grew up in a Western culture and, therefore, studied science using a Western language.

It's my assumption that's the frame in which the question was... well, framed.
 
  • #17
jobyts said:
Our marketing team always wanted 3 letter acronyms for the all our product names.

The Ramans do everything in threes.

Arthur C Clarke
 
  • #18
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...
 
  • #19
But in scientific writing, the commas aren't used at all.
 
  • #20
BobG said:
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.
waht said:
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
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)
 
  • #21
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-.
 
  • #22
FrancisZ said:
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)

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."
 
  • #23
Jack21222 said:
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."

It isn't illegal. It's just impractical.
 
  • #24
FrancisZ said:
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).

That's not true. In British a billion is a million million, and a trillion is a million billion. Of course, no one really uses these anymore, but instead uses the American terms.
 
  • #25
cristo said:
That's not true. In British a billion is a million million, and a trillion is a million billion. Of course, no one really uses these anymore, but instead uses the American terms.

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.
 
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  • #26
It only makes sense to have a comma after 3 digits. It would make things unnecessarily complicated if you put a comma after every four digits. 1 million would be 100,0000.
 
  • #27
If you put a comma after every four digits, your naming system wouldn't be based on three digit increases
 
  • #28
Office_Shredder said:
If you put a comma after every four digits, your naming system wouldn't be based on three digit increases

You sure you know which came first?
 
  • #29
leroyjenkens said:
You sure you know which came first?

It doesn't matter. Whichever came first obviously influenced the other one. They probably evolved at the same time.
 
  • #30
leroyjenkens said:
It only makes sense to have a comma after 3 digits. It would make things unnecessarily complicated if you put a comma after every four digits. 1 million would be 100,0000.
In the traditional Chinese system, a million is 100 wan, that is 100,0000.

Office_Shredder said:
It doesn't matter. Whichever came first obviously influenced the other one. They probably evolved at the same time.
The names kilo and mega were used in Ancient Greece, long before the Arabic system was invented. The names billion and trillion weren't used before the 15th century, long after it was invented.
http://en.wikipedia.org/wiki/Names_...ins_of_the_.22standard_dictionary_numbers.22"

Here is some more interesting information.
wiki said:
For ease of reading, numbers with many digits before or after the decimal separator may be divided into groups using a delimiter, with the counting of groups starting from the decimal separator in both directions. This delimiter is usually called a thousands separator, because the digits are usually in groups of three, that is, thousands. The most general name for this delimiter is digit group separator, because thousands are not always the relevant group. For example, in various countries (e.g., China, India, and Japan), there have been traditional conventions of grouping by 2 or 4 digits. These conventions are still observed in some contexts, although the 3-digit group convention is also well known and often used.
http://en.wikipedia.org/wiki/Decimal_separator"
 
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