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As I understand, Japanese numbers are divided into blocks of four, so while we would think of the number 89123889 as 89,123,889, in Japan they would think of it as 8912,3889 (八千九百十二万三千八百八十九). So English uses thousands and Japanese uses tens of thousands.

Is there any particular reason for this? Not that it matters either way, I'm just wondering at what point either culture chose to delimit numbers by thousands, or tens of thousands.

If you reply with Japanese, please use hiragana and furigana only, except for number kanji.

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India does this too, except with 100,000. en.wikipedia.org/wiki/Lakh –  Chloe Jun 1 at 5:52
    
Does what, delimit by four? –  Leo King Jun 1 at 7:23
    
@Chloe The Indian system isn't all that similar. At least for currency, the basic units are 10^3 (thousand, or the equivalent in a local language); 10^5 (lakh); 10^7 (crore); and then stacking those together (10^11 = ten thousand crore, 10^12 = one lakh crore, etc.). It's not all that similar to the Japanese system, since the spacings are uneven, and there aren't special names (in use, anyway) for anything higher than 10^7. –  senshin Jun 1 at 13:41
    
Related question on math.se (and not answered, sadly). –  jmac Jun 2 at 4:31
    
And a very interesting question, too, thanks for the link! Hope it gets answered. –  Leo King Jun 2 at 8:10

5 Answers 5

up vote 18 down vote accepted

This is a summary of this Wikipedia article.

A math book called 塵劫記【じんこうき】 published in 1627, was the first book that described (and probably defined) how to count large numbers in Japanese.

In the first edition of the book, actually there was no "4-digit grouping" as we know today, at least for relatively small numbers (smaller than 1 極【ごく】). A different kanji was used for each digit. 104 was 万, 105 was 億, 106 was 兆 ... and so on, until it reached 1 極, which was only(?) 1015.

Soon after that, the 4-digit grouping was introduced in a revised edition of 塵劫記 published in 1631, and 1 極 bacame 1048. In this edition, 8-digit grouping was still used for numbers even larger than 1 極 (100000000 極 = 1 恒河沙【こうがしゃ】, 100000000 恒河沙 = 1 阿僧祇【あそうぎ】, and so on)

In a year 1634 edition, the 8-digit grouping was completely removed, and the simple 4-digit grouping system after 万(=104) remained. This is exactly how Japanese count large numbers today.

Before 塵劫記, Japanese had relatively small vocabulary for big numbers, and 万【よろづ】 (=104) seems to be the largest unit. 八百万【やおよろづ】 meant "countless."

This 4-digit loop is borrowed from Chinese numeric system. Korea also uses a similar system. However I couldn't find why and when Chinese started to use 4-digit scale instead of 3.

(By the way, I was surprised that English-speaking people used long (6-digit) scale until relatively recently.)

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Really informative, well-researched answer, nice one! Very interesting, too :). And just on a side note about the long and short number scales, we still sub-divided numbers into 3 digits. It only changed how we read the numbers 1,000,000 and larger. –  Leo King May 31 at 20:48
    
This also explains all those 万~ compounds –  ssb Jun 1 at 23:55

Numbers in English and most "western" languages are still influenced by Roman numerals, where 1000 = M = mille was the largest number that had its own, non-compound name.

Japanese took its numerals originally from Chinese, where there is a separate character for "ten thousand". It also has characters for larger numbers, but groupings of 5 or more are probably less convenient as they are harder to recognize quickly.

However, neither system historically came into being fully complete and used consistently. Both changed through the times and there were conflicting usages for a long time until everyone converged on a standard.

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Koreans do it this way too, being based on Chinese. They have a single word, 만, meaning ten thousand. Then for hundred thousand they say literally ten-ten thousand, 십만, for million they say literally hundred-ten thousand, 백만, and so on. So the numbering system is logically split into clusters of 4 digits, not 3 as is the case in the United States and others. –  Michael Munsey Jun 1 at 17:56

in Japan they would think of it as 8912,3889 (八千九百十二万三千八百八十九).

Just FYI, no one in Japan writes numbers like that. Maybe you can find a museum or similar re-creation that does it when the tourists are watching, but retail, business, banking, government etc. use western formats.

The only place you will regularly see much smaller numbers written in kanji is on restaurant menus and addresses on new years cards, when the writer is going for an old-fashioned look, like Fraktur in Germany:

とんかつ:一千二百円

東京都品川区上町二丁目十七番9号

but the address is much easier to type as 東京都品川区上町2-17-9

If you are learning this archaic writing method for the end purpose of reading pre-Meiji works in the original Klingon, keep studying. If you are learning modern Japanese for the purpose of working in or with Japan, you already know more than you will ever use. Move on to useful things.

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in the original Klingon?? –  hippietrail Jun 1 at 5:09
    
Hey, ease up, I've been learning very basic entry level Japanese:p –  Leo King Jun 1 at 7:46
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Then you're wasting your time. Learn katakana, then useful vocabulary. BTW most learn-japanese texts are less than useful - Japanese for Busy People is the most practical I've seen. –  paul Jun 1 at 11:02
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But you do need, at a minimum, to be able to understand spoken numbers. –  snailboat Jun 1 at 11:56
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It is true that Arabic numerals (0, 1, ..., 9) are generally preferred today, but Leo King was explaining how Japanese people read and understand big numbers like "89123889". It is natural to use 漢数字 here; 八千九百十二万三千八百八十九 is easier to read than はっせんきゅうひゃくじゅうにまんさんぜんはっぴゃくはちじゅうきゅう. Anyway, you can mix kanji and arabic numerals to comprehensibly write big integers. You can write "7654億8912万3889", which is more understandable than "765,489,123,889" to Japanese. –  naruto Jun 2 at 5:14

More than likely it is borrowed from Chinese.

十 百 万 亿[億] 兆 京

respectively:

10^1, 10^2, 10^4, 10^8, 10^16, 10^32 etc. (goes on until 10^4096 !)

I have seen 亿 and 兆 used in these definitions in modern Chinese and Korean, and certainly 億 in japanese for money e.g. 三億円 meaning 3 x 10^8 yen.

This system of creating a new word whenever the length doubles seems natural, as it is the minimal set of words you need to represent any arbitrarily large number without repeating yourself. It also provides a more unique way to say a number. For example, in english we could say one million billion == 10^15 == one thousand trillion).

This has changed in modern china... 亿,兆,京 now sometimes mean smaller powers in different contexts for convenience. 兆 can mean a megabyte (10^6), e.g. 四十兆 => 40 Megabytes. Not sure if Japanese has this ambiguity, but 千 (10^3) certainly exists and doesn't fit the 'pure' traditional system.

In any case, I have never seen a split into blocks of 4 when writing a number down. But that is the logic that should be used when reading a number out.

That is misleading though, since even larger numbers should be read by recursively bisecting at the highest 10^2^n which fits, and this can get a lot more abstract than simple powers of 10^4. To choose an unrealistic example:

1,000,020,000,304,567 =>

10000200 * 10^8 + 00304567 =>

1000,0200 億 30,4567 =>

(1000 * 10^4 + 0200) 億 + (30 * 10^4 + 4567) =>

(1000 万 200) 億 (30 万 4567) =>

(一千 万 二百)億(三十 万 四千五百六十七)

Please note it is different than just separating with length 4 blocks: 10^12 does not have a unique name, but 10^16 does. So it really is unlike the western system. Blocks are only assigned a new name when they reach twice the length of the last named block. Rather than just 3,6,9,12,15, we have 4,8,16,32.

For negative powers of 10, the western style of 10^-3, 10^-6, 10^-9 is used... (equivalent to milli/micro/nano).

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10^4096? Maybe the Chinese wondered how many protons there would be in the universe, if in every proton there was a whole universe with the same number of protons, and in every one of those protons, there was a whole universe with that many protons, and in those protons there were again a whole universe, etc. –  Earthliŋ Jun 1 at 20:40
    
Wow, that's such a cool system :). Thanks for the information! –  Leo King Jun 1 at 20:56
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It's possibly a bad sign that the first thing I'm reminded of is 2048, though... –  Leo King Jun 1 at 21:06

To add to the previous answers, the rule is Arabic numbers for horizontal writing:

123456789

and Chinese numbers for vertical writing.





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