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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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orthography numbers
Is there a reason why numbers in Japanese are delimited into blocks of four?
The following is a summary of [this Wikipedia
article](http://ja.wikipedia.org/wiki/%E5%91%BD%E6%95%B0%E6%B3%95).

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](http://dbr.library.tohoku.ac.jp/infolib/user_contents/wasan/l/j001/06/j001060007l.png),
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 assigned to 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 became 1048. In this edition, 8-digit grouping
was still used for numbers 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 the [year 1634 edition](http://mahoroba.lib.nara-
wu.ac.jp/y05/html/380/l/p006.html), the 8-digit grouping was completely
removed, and the simple 4-digit grouping system after 万(=104) remained. This
is exactly how the Japanese language count large numbers today.

Before 塵劫記, Japanese had a relatively [small
vocabulary](http://www.sf.airnet.ne.jp/ts/language/number/ancient_japanesej.html)
for big numbers, and 万【よろづ】 (=104) seems to have been the largest unit.
八百万【やおよろづ】 meant "countless."

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

(By the way, I was surprised to find that English-speaking people used [long
(6-digit) scale](http://en.wikipedia.org/wiki/Long_and_short_scales) until
relatively recently.)
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Numbers in English and most "western" languages are still influenced by [Roman
numerals](http://en.wikipedia.org/wiki/Roman_numerals), where 1000 = M =
_mille_ was the largest number that had its own, non-compound name.

Japanese took its numerals originally [from
Chinese](http://en.wikipedia.org/wiki/Chinese_numerals#Large_numbers), 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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> 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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To add to the previous answers, the rule is Arabic numbers for horizontal
writing:

> 123456789

and Chinese numbers for vertical writing.

> 一  
>  二  
>  三  
>  四  
>  五
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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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