While it seems quite illogical, most numbers are grammatically singular. It's also the difference between those that take Nominative (trzy psy) and those that take Genitive (pięć psów). If the number takes Genitive, it also takes verbs in singular.
The nouns that take Nominative are: 1, 2, 3, 4 and those that end in -2, -3, -4 - BUT NOT those that end in -12, -13, -14. All the others take Genitive.
Firstly, "dwy" is definitely not a word ;)
Secondly, most numerals are actually grammatically singular. You have "dwa koty są" (two cats are), but "pięć kotów jest" (lit. "five cats is").
You probably are aware that some numerals take Accusative (dwa koty), but most take Genitive (pięć kotów). As a reminder, Accusative is used for 1, 2, 3, 4 and the numbers ending with -2, -3, -4 BUT NOT -12, -13, -14. Complicated. Anyway, those that take Genitive are also grammatically singular.
So to conclude, for "100 000 002" should use "są", true. And I kinda started writing this thinking it will be "jest". Which proves how hard Polish numerals are. But you also really rarely have to say things like "sto milionów dwa koty". Reaaaally rarely.
Oh, one more thing. Just "sto milionów" works perfectly fine because with such a round number you just automatically assume it's about money. But if I heard "Gdzie jest moje sto milionów dwa?", I would be very confused, because it suddenly is not round anymore and I have no idea what you're talking about, as there's no noun.
In the end, I still speak too little Polish to make a worthwhile comment, and less do I know about Slavic languages, but thanks a lot for your comment! I also found a seemingly interesting article about the Polish numerical system that might answer the question about why numbers from one to four and those following thereafter are distinguished in terms of the grammatical case. But I didn't manage to read it yet, which I expected to do the day before which is the reason why my response follows belatedly. In case you should be interested in reading it, here's the link: https://www.glossa-journal.org/articles/10.5334/gjgl.880/ I do not know the journal so that it could also be a waste of time, but the predicate of having been peer-reviewed hoists my hopes and regards.
As for the “finger issue”, I think that I will look for an etymological dictionary of the Polish language as soon as I find some time. It might help to firstly trace back the (original) meaning of the words “parst” and “pirst”. Hopefully something like this exists, I once used to look for an etymological dictionary for the Russian language but surprisingly, my discoveries were scarce, in spite of the vast amount of speakers and the felt popularity of the language.
Seriously, who was in charge of constructing the Polish numerical system? I have to have a word or two with this tortuous sadist... Even the French numerical system is not even half this complicated, and I met many people complaining about the construction of numbers like eighty (quatre-vingt) or ninety (quatre-vingt dix).
who was in charge of constructing the Polish numerical system?
Well, it is Tradition, and in fact very, very old tradition - as proper numerals disappeared from Proto-Slavic language before it developped into regional dialects of Slavic languages. So our ancestors had to deal with it somehow. And since at that era a person did not "have" 5 fingers at one hand, but 1 thumb ("kszciuk") + 4 fingers ("parst" or "pirst") - therefore numerals up to 4 were described as adjectives up to the number of "parst", i.e. 4, while above 4 - our ancestors used nouns, which is not that strange (in English "hundred" also behaves as a noun, in a way).
And that is why the numbers ending with 1,2,3,4 have "adjectival" declension, and numbers ending with 5,6,7,8,9 have substantival declension.
And here is an in-depth article about syntax with numerals: http://grzegorz.jagodzinski.prv.pl/gram/pl/liczeb02.html (in Polish, and you probably need an ad-blocker to work with that text)
Of course I knew that you were joking, but the problem is interesting. And more complcated... E.g. there are traces in the language that permit to suspect, that in Early Midieval Polish only the thumb was actually considered a finger - there are several ancient Polish proverbs about "being alone as a finger"or "naked as a finger" etc, which seemingly referred to the thumb. What were the other? I do not know. Maybe "parst" or "pirst" meant "lesser fingers"? There are however some nouns derived from them, e.g. "naparstek" ("na + parst") = thimble; "pierścionek" ("pirst + onek") = ring (a piece of jewellery) - see: https://obcyjezykpolski.pl/zostaniesz-kiedys-sam-jak-palec/
Actually, my comment was not meant that serious, as I already lack the knowledge to make an informed statement about Slavic languages (in the end, I studied English, not Russian, or Serbian). But does this rule of the numbers one to four are Accusative while those following thereafter are Genitive from our thumbs and fingers? I opine to remember that in PIE, there existed no word for thumb, as it was likely considered the fifth finger, but I may be wrong.
(In a way, yes, I never truly thought about how in Germanic languages numbers behave, or are treated; a good question, actually, it might depend on the individual sentence and the numerical word's position in relation to the described noun, or whether it is understood as a noun)
However, thanks for your your informative comment, I also saved the Polish article (my Adblocker is activated by default already), I appreciate it!
Not sure what you're asking about... Well, "Where is my one million?" = "Gdzie jest mój milion?", for example.
Forget the millions, because it could be cows for what it's worth, it's neuter because of "sto". Gdzie jest moje sto [milionów/krów/milionów krów]? Gdzie są moje dwadzieścia trzy [miliony/krowy/miliony krów]?
I was thinking of money at this sentence, because if it were about cows, that would be mentionned, so "where are my one hundred millions" seems quite natural to me.(or maybe I watch too many gangster mowies) I guess this sentence is just used for grammatical purpose, and like often, in a conversation you would not use the same words to express the same thing. how would you say in polish to ask for your 100 000 000 (zloty)? thanks
Well, although it is possible to interpret this sentence using something else than money, as there is no noun, the intention behind it is definitely about money. But it could be clarified by saying "Gdzie jest moje sto milionów złotych?!".
This is a reference to Lech Wałęsa's promise during the presidential campaign of 1990, when he said that everyone should get 100 000 000 złoty. 1 dollar at that time cost, from what I googled, around 9500 złoty, so we arrive at more than 10,5 thousand dollars (1990 dollars, of course). Well, sounds like a ton of money to me. Somehow this promise wasn't fulfilled...
In 1992 Kazik, a very popular singer in Poland, recorded a song "100 000 000" which refers to that promise.
thank you Jellei, maybe you'll get 100 000 000 lingots. I really like this currency! by the way thank you to duolingo, i do not know any other site where you can really learn a language for free, maybe https://www.espagnolfacile.com, but the choice is very limited and no polish. I'll try to find the song on youtube. in many countries the basic income is discussed and who knows, it could come true. :-)