Rendaku causes roppyaku?

According to Wikipedia, a phenomenon known as Rendaku causes 600 (for example) to be pronounced roppyaku instead of rokuhyaku. This is not new to me, but I do wonder why it be Rendaku that causes this, since Rendaku doesn't appear to make such changes; it only changes a voiceless consonant into a voiced one under certain circumstances.

A little background: I'm in the process of writing a small web application that can convert numbers into their Japanese pronuciation and it would be cool if the algorithm that creates the pronouciation is completely generic without any "hard coded" exceptions.

I can easily make function that applies rendaku as described on Wikipedia.

But the real question is: what rule causes rokuhyaku to become roppyaku, or ichichou to become icchou (a trillion, iirc)? Or are these truly exceptions that need to be implemented as such? I think Rendaku is not it, because neither Wikipedia nor any other source I found describe the transformation that happens in a number like 600.

I hope I explained my poblem clearly. If not, I apologize.
Thanks for any help :)

sanbyaku, yonhyaku, roppyaku, nanahyaku, happyaku, kyuuhyaku.
They are distinct & easier to differentiate when you hear.
Also, shijyuu, shichijyuu are read so for (older) proper nouns, i.e. property, street, etc. but they are read yonjyuu, nanajyuu in numbering so to avoid confusion, shi vs shichi

Some of the number pronunciations are not right here:
http://wiki.answers.com/Q/How_to_say_1-100_in_japanese_correctly

I know who to say numbers in Japanese, and I know how and where to apply such tranformations. What I'm looking for is a written rule that states exactly when to apply such transformation, how to apply them, and when not to.

In your examples, namely sanbyaku and roppyaku, you're already two different kinds of transformations. In sanbyaku, Rendaku is applied, which converts the voiceless first consonant into a voiced once (hi becomes bi).

But in roppyaku something different happens that is not Rendaku by any definition I know. The last syllable of the first part (ku in roku) becomes a Suokon, geminating the following consonant, which by chance is also transformed from hi to pi.

If you think about it, the change from "hya" to "bya" or "hya" to "pya" is very close - in hiragana, they are represented as "hya" ひゃ "bya" びゃ and "pya." ぴゃ.

You can assume that the change from "h" to "b" happens with the number 3, and the change from "h" to "p") happens with the number 6 and 8.

If you think of adding counters to the numbers, such as "-hon" (for counting long things), the same happens:
ippon, nihon, sanbon, yonhon, gohon, roppon, nanahon, happon, kyuuhon, juppon.

For counter "-hiki" (for countring small to medium sized animals):
ippiki, nihiki, sanbiki, yonhiki, gohiki, roppiki, nanahiki, happiki, kyuuhiki, juppiki.

(Actually with counters, the same happens with the number 1 and 10, but with numbers (without counters), you don't have to worry about that.)

Well, yes and no I guess :)

I do understand how hya becomes bya. Just add ten-ten. What I don't unsterstand is how ichihon becomes ippon. Yes, it's because it sounds better. Got it. But by what *rule* is it transformed that way?

ichihon--ippon is certainly not a simple matter of adding ten-ten. It's a matter of dropping a whole syllable, adding in a Suokon, and adding maru instead of ten-ten.

I'm wondering what rule causes this exactly.

Ummm, it's not really because it sounds better, but it is "easier" to say it that way, which later turned into an established convention.

If you take "ichi" "hon" and say it slowly, you will notice that the movement of the lips is quite a lot - pulling the lips sideways with the "i" at the end of "ichi" and then rounding the lips to form the "ho" sound. If you say it fast, you will be saying something that sounds like "icchon." So ... I cannot find anything that explains exactly how and when it happened, but it became a convention to shorten it to "ippon" I suppose.

With the ones that change from "h-" to "b-," that is more easily explained because, let's say, with the word "san" "hyaku," you almost close your lips with "n" at the end of "san"so it's easier if you start the next syllable with the lips closed ("b") rather than opening them once to say "hyaku."

I guess for a Japanese person it would be harder to say. My sensei told me her grandparents cannot even say the word CD (pronounced as "siidii") which is logical since those syllables don't exist, and they say something like "seidei".

Anyway. I suppose I can deal with those words like icchou and ippon, and such, as being true exceptions in the language? There's no rule that reliably determines when and how to transform word combinations, and when not to?

I think you are right in considering that "rokuhyaku" becoming "roppyaku" is not explained only by Rendaku.
And I see by "Suokon" you mean "Sokuon." Sokuon is written in kana as "tsu" but practically in the pronunciation it's a short stoppage with the breath held for a moment.
Here I use an expression "Sokuon-ka" to mean a change of a syllable to Sokuon.
e.g. "Torite" becomes "totte" (= knob, handle). "Sakuka" becomes "sakka" (= creator of art, such as novelist).

what rule causes rokuhyaku to become roppyaku

A Japanese syllable beginning with a phoneme [p] is called "Handakuon," which literally means a half-voiced sound. I understand the changes of [f] / [h] to [b] and [p] are both types of Rendaku.
I suppose it can be said that two phenomena, Sokuon-ka and Rendaku, happen when "rokuhyaku" becomes "roppyaku": a syllable [ku] for "roku" becomes Sokuon and a phoneme [h] for "hyaku" becomes [p]; the same can be said as to "ichi-hon" becoming "ippon."

I am not sure how [p] came to appear in Rendaku. But I feel the change of [f] to [p] easier to understand than that of [h], especially in a case Sokuon-ka also happens. Trying to repeat "kirifu" rapidly with one accent on [fu], I gradually make it like "kiffu" (i.e. [ri] becomes Sokuon) then like "kippu" (i.e. [f] becomes [p]).
Maybe the change of [h] to [p] is related to that the first phoneme of syllables which is now pronounced [h] was closer to [f] in old Japanese.

I'm in the process of writing a small web application that can convert numbers into their Japanese pronunciation

" 四 " , " 七 " and " 九 ", when they are before " � " or " 百 " or so, are usually pronounced "yon," "nana" and "kyuu."
In some idiomatic cases, a number is read in another way.
e.g. " 四� " in a word, when it forms a number referring to age of a person / people in 40s, can also be read "shijuu."
e.g. A word " 四暑纉� ", when meaning the biggest Buddhist memorial service for a deceased on the 49th day of the death, is read "shijuuku-nichi," not "yonjuukyuu-nichi."

it would be cool if the algorithm that creates the pronunciation is completely generic without any "hard coded" exceptions.

As to numbers themselves, rules are simpler than when they are with counters.

[ � juu (= ten), pronounced "juu"]
Pronunciations of " 二 " to " 九 " have no change when they precede " � ."

[ 百 hyaku (= hundred), pronounced "hyaku" / "byaku" / "pyaku"]
-- hyaku ( 百 ), sambyaku ( 三百 ), roppyaku ( 六百 ), happyaku ( 八百 ).

[ 千 sen (= thousand), pronounced "sen" / "zen"]
One thousand is usually pronounced "sen." To emphasize "one" we use 一千 .
-- sen ( 千 ) / issen ( 一千 ), sanzen ( 三千 ), rokusen ( 六千 ), hassen ( 八千 ).

[ 万 man (= ten of 千 ), pronounced "man"] and
[ 億 oku (= ten of thousands of 万 ), pronounced "oku"]
Pronunciations of " 一 " to " � " , " 百 " and " 千 " have no change when they precede " 万 " or " 億 ."

[ 兆 chou (= ten of thousands of 億 = million of millions), pronounced with a prolonged "o"]
-- itchou ( 一兆 ), sanchou ( 三兆 ), rokuchou ( 六兆 ), hatchou ( 八兆 ).
-- jitchou / jyutchou ( 薯� ), hyakuchou ( 百兆 ), sambyakuchou ( 三百兆 ), senchou ( 千兆 ), sanzenchou ( 三千兆 ).

[ 京 kei (= ten of thousands of 兆 ), pronounced with a prolonged "e"]
-- ikkei ( 一京 ), sankei ( 三京 ), rokkei ( 六京 ), hakkei ( 八京 ).
-- jikkei / jyukkei ( 暑� ), hyakkei ( 百京 ), sambyakkei ( 三百京 ), senkei ( 千京 ), sanzenkei ( 三千京 ).

(Here I avoid "trillion" / "billion" because it means the other number in (old) British English, French, German (and maybe other European languages) than in American English.)

Sorry, I clicked "submit" a bit too early.
-- NOT: "tsu" ; BUT: small "tsu"
-- NOT: "trillion" / "billion"; BUT: trillion and billion
-- NOT: it means the other number; BUT: they mean other numbers
Thanks.

Similar to ''happon'' as AK said, you'll also find ''happou'' (hachi + hou) in martial arts a lot.

はっぽう [八方] (n) all sides

And what about that famous place in Tokyo, Roppongi! 六本木

If you find the name of this ''rule'', let us know. For now, we can think of it as a ''rendaku contraction''.

Excellent explanation. Thanks :)
I'll dive into it soon and see if I can conjure an algorithm that does this task of "rendaku contraction" ;)