Is there an indicator that the numbers are being given in fivers? In Spain we would often price things in duros, and before I was old enough to get an allowance in perras chicas or perras gordas (all of them were different coins, and even different coins at different points in history), but said the unit.
(Just adding on)
There is, in fact, an entire Japanese counting system separate from the Chinese based one. “Hatachi” “yon” and “nana” are part of those artifacts. When you get into how you actually count objects in Japanese you enter a world of bullshit that throws the Japanese “perfectly nice” counting system out the window.
Different objects have different counting suffixes. So, for instance, if you’re counting cylindrical objects (soda cans, salt shakers, whatever), you get:
ippon, nihon, sanbon, yonhon, gohon, roppon, …
Don’t worry about the pon, bon thing, that’s just a Japanese sound change phenomenon and not too weird.
(Special note: confusingly, the kanji for this is the same as the kanji for books, which you’d count with satsu. My completely ad hoc folk etymology is that maybe books used to be on scrolls or something, but for all I know it’s arbitrary or comes from one of the other Kanji meanings)
What is weird, is that while most counters follow that pattern fairly precisely, there are a few… notable exceptions.
If you’re counting people, the first two are
hitori, futari
Followed by
sannin, yonin, gonin (etc)
The other noticeable one is the ending -tsu which is generally for counting objects that don’t fall into a common counter bucket.
hitotsu, futatsu, mittsu, yotsu, itsutsu, muttsu, nanatsu, yattsu, kokonotsu, tou
Never mind that tou drops the tsu pattern, where the hell did that come from? You may recognize (yo)tsu and (nana)tsu from before! They’re the traditional Japanese counting numbers! Fossilized in a couple places like this. In case you’re wondering, “hatachi” is, indeed, 20. (Someone can add on, but I think this is usually only used for small numbers, above 10-ish I think the counter ko is used with Chinese numerals when no counter exists).
Days of the month is also problematic. The first is “tsuitachi”, which is apparently a corruption of the archaic “tsukitachi” (lit. beginning of the month). The next is futsuka, mikka, yokka, … Japanese numbers to touka. Then Chinese numbers followed by -nichi (e.g. juuichinichi for 11) for the rest. Because… because language, that’s why.
This isn’t even getting into the not-illogical-but-confusing-for-English-speakers larger numbers, which is sort of 10,000 based. You have a word for “hundred”, then “thousand”, then “ten thousand”, then it’s combinations of these (e.g. “thousand-ten-thousand” = 10 million) up until a new word at 100 million (a.k.a ten thousand ten thousands) and 1 trillion (ten thousand 100 millions). I think a lot of this (and the counters) comes from Chinese influence, though.
There’s also something weird with ordinals (first, second), but I can’t actually remember when you use which counting system, so I won’t go over it.
So yeah, TLDR version: Japanese numbers are only simple if you never want to actually use them except for maybe counting currency or impressing your friends.
Well, “tres” comes from the word for “three,” fjerds from the word for “four,” etc.
I know what the “half” means, in this context; most Scandinavians don’t. See, they use “half” like that only to indicate time (as you say), and wouldn’t think of using it any other way. The “oh and of course you’re also supposed to multiply by twenty” addition comes seemingly out of nowhere, too, since no one says “tresindstyve,” “firsindstyve” or “femsindstyve” anymore, and there’s nothing quite like it it any other Scandinavian language anyway.
Thai numbers are very straightforward, but with a quirk or two. 2300 would be two-thousand-three-hundred, often abbreviated to two-thousand-three. Similarly, 23,000 would be two-tenthousand-three. Leading ones are often omitted, so 1200 is just thousand-two.
Quirks: [ul][li]Counts, especially one, often go after a noun, so although thousand-two means 1200, thousand-one usually means just 1000, not 1100. A more complete construction (one-thousand-one-hundred, or eleven-hundred) is needed when the first two digits of a number are both 1![/li][li]Many technical Thais avoid any confusion by using two digit-counts, e.g. twentythree-thousand for 23,000 instead of two-tenthousand-three.[/li][li]Since the words for 2 and 3 are similar, an alternate for 2 (/tho/) is sometimes used when, e.g. reciting a phone number.[/li][li]Two-digit numbers are built in straightforward fashion from the one-digit numbers, except for 11, 21, 31, 41, etc. in which a different syllable (/et/) is substituted for the usual one (1 = /neung/). However, /et/ can be confused with the word for 8, so /neung/ is sometimes used by military, etc. (And a Lao word for twenty is often heard in some parts of Thailand.)[/li][li]After a taxi took me to 18th Lane when I wanted to go to 11th Lane, I started using sip-neung for 11 before knowing that was the military recommendation. 
[/li][/ul]
On a tangent to the OP’s question:
I am an unashamed conlanger (one of those people who makes up languages for no good reason), and in one of my older ones, Savin, there were no numbers at all, only expressions of quantity in terms of the speaker’s needs or expectations. Thus, you have words for…
nothing / none
far less than expected, such that the deficit is a problem
far less than expected
less than expected, but not too little
far too little / way too few
too little / too few
just short of the right amount
exactly enough / the right amount / exactly what is expected
a touch over the right amount
too much / way too many
far too much / far too many
more than expected, but not too much
far more than expected
far more than expected, such that the surplus is a problem
everything / all
The number of speakers of Savin? To you, exactly what you expect. To me, far too few. To anyone else, none.
I can’t quote the exact tribe and language, but I recall that some Papuan tribes count one, two, many!
In Arabic they have the concept of one, two, many in suffixes. For instance Moslem means one person, Moslemoon means two people, Moslemeen means more than two people.
Jragon put it very well. I would only add that, indeed, “counters” are also used in Chinese, and that you can think of them as applying to everything constructions like the English “3 heads of cattle” (where the “counter” would be the word “head” in this case). I would imagine that the use of “counters” in Japanese are a direct Chinese influence.
The underlying numbers are always the same, though.
For the sake of completion, here go the full set of “native” Japanese names for the numbers. The units have a “-tsu” ending, which can be changed if the thing being counted changes (see the “hitori”, “futari” mentioned by JDragon):
(NB: The “ou” indicates a long “o”).
1 - hitotsu
2 - futatsu
3 - mittsu
4 - yottsu
5 - itsutsu
6 - muttsu
7 - nanatsu
8 - yattsu
9 - kokonotsu
10 - tou
When using “native” numbers in Japanese, 99% of the time only numbers between 1 and 10 will be used (the first days of the months, counting generic objects up to 10, counting one or two people).
There are ways to build numbers above there, though (and, as mentioned by Sage Rat, there is the use of “hatachi” to express “20 years of age”). And they tend to follow the simple “add unit after tens” pattern (although the names for the tens and the hundreds appear to follow slightly irregular building patterns, though).
As mentioned, you will almost never see these numbers used, except for “hatachi” and the word for 8000, which appears in the lyrics of the Japanese national anthem. Sometimes you might find somebody writing really fancy poetry or something like that, where they go and use these terms… But you won’t see them in everyday life.
11 - tou amari hitotsu
12 - tou amari futatsu
13 - tou amari mittsu
…
18 - tou amari yattsu
19 - tou amari kokonotsu
20- hatachi
21 - hatachi amari hitotsu
…
30 - misoji
40 - yosoji
50 - isoji
60 - musoji
70 - nanasoji
80 - yasoji
90 - kokonosoji
100 - momo
200 - futao
300 - mio
400 - you
500 - io
600 - muo
700 - yao
900 - kokonou
1000 - chi
2000 - futachi
3000 - michi
4000 - yochi
5000 - ichi
6000 - futachi
7000 - nanachi
8000 - yachi <– appears in the lyrics of the Japanese national anthem
9000 - kokonochi
10000 - yorozu
(and so on, building “name”+yorozu for 20000, 30000, etc)
I still think that the Sino-Japanese numbers are easy to build, though 
The dual number. Proto-Indo-European had it too, but none of the IE languages still have it. Ancient Greek had it and I think Vedic Sanskrit had traces of it. Hebrew had the Semitic dual too, in prehistory, but by the time it was written it survived in only a few words that came naturally in pairs. Arabic is pretty much the only language left with a functioning dual.
As for the endings…
A Muslim = مسلم muslim
2 Muslims = مسلمان muslimān
3 and up = مسلمون muslimūn
Arabic numerals have their own weirdness, not in the numbers themselves, but in how they are applied to nouns. From 3 to 9, masculine plurals agree with numbers that have the feminine ending, and feminine plurals agree with numbers that don’t have it. For 10 and up, all plurals are treated as feminine singular for purposes of numeric and adjectival agreement, except for nouns that denote male rational beings, which get the masculine plural. Actual *plural *feminine plurals are for female rational beings. Some feminine nouns about abstract concepts get the feminine plural ending, but still take the feminine singular agreement.
There are remains of it, especially in the Baltic and Slavic languages.
Standard Slovene keeps it in nominative and partially in other cases (One wolf: volk - Two wolves: volkova - More than two wolves: volkovi).
Russian also keeps traces of dual in the plural forms of certain body parts (One eye: glaz - The two eyes in your face: ochi). A very interesting word is the word for “knee”, which happens to be the same as the word for “tribe of Israel”: koleno. If the intended meaning is “knees”, the plural for “koleno” is “koleni”. If the intended meaning is “tribe of Israel”, the plural is “koleni”.
Mostly, but for one thing y’all left out: an original word, “man”, for “ten thousand” as a unit of counting. So, in Japanese, you don’t have “two hundred thousand”, you have “twenty ten-thousands”.
On edit I see that it actually did get mentioned, but I’ll leave my post to highlight both the strangeness of the Japanese counting system and my own idiocy.
Thinking of it a different way, it’s the difference between putting commas after every 3 zeros vs every 4 zeros, i.e.
1,000,000,000,000 vs 1,0000,0000,0000
It’s just there’s not usually a simple, single word in Indo-European languages for 1,0000.
I think (but am not sure) it’s not uncommon to see this type of notation on occasion.
It does make translation a bit of an issue with East Asian languages. Sometimes I’ll have to do some mental translation when my parents say something about a hundred thousand (in English of course) when they really mean a hundred ten-thousands, i.e. a million. Or they’ll slow down when dealing with large numbers because they have to translate between 4-zeros thinking and 3-zeros thinking.
Absolutely fascinating intersection between simple arithmetic/number theory and cognitive science and linguistics.
That’s the one I was going to mention, having learnt a little Slovene on my time out there and being fascinated by the dual number, but I’ve also been told that Sorbian preserves the dual (and googling it seems to confirm.)
And I see, long after I posted this, that I made a tremendously stupid boo-boo. The plural of “koleno” when it means “knees” is indeed “koleni”; the plural of “koleno” when it means “tribe” is “kolena” :smack:
My apologies!
Actually, to a certain extent there is – The word “MYRIAD”, which comes straight from Greek and means “ten thousand” (and is the origin of the prefix “myria-” that was proposed by the French when the Metric System was thought of).
Also, interestingly, when Archimedes had to deal with really big numbers in some of his mathematical work, he developed a system that boils down to what the Sino-Japanese numerals do – going up to myriads and then “myriads of myriads” and “myriads of myriads of myriads”
I was taught in (American) English class that the only place appropriate to use the word “and” was between whole numbers and fractions. The teacher’s explanation was, when you say, “One hundred and fifty people,” we don’t know what the one thousand refers to: One thousand what’s and fifty people?
That was in seventh grade. When I was in high school, when we were taught how to write a check, that the only place to use “and” was between the dollars and cents. So, the pre-printed check wuold have a blank line ending with “Dollars”, and we were to write, “One thousand, one hundred eleven and 11/100” before the word dollars. There wouldn’t be room on that line to write “One thousand AND one hundred AND eleven AND 11/100”
As I understand the English English way is to use the “and” only before the tens (and ten thousands, and ten millions, etc.) column value:
One hundred AND forty-three, or ten million, three hundred AND seventy-six thousand, eight hundred AND twelve. Why not then write it, “ten million AND three hundred AND seventy-six thousand AND eight hundred AND twelve”?
What do you do when you have a fraction? Do you still use “and” for that?
This is some weird grammar voodoo and is not consistent across the US. I was never taught that rule, and hearing “and” in the middle of a number was not unusual. For example, Disney’s “101 Dalmatians,” pronounced as “one hundred and one Dalmatians.”
Both Spanish and French use the one and ten, two and ten, three and ten, etc… system. It’s just that the latin wor decim “sligtly” evolved into “ce” and “ze”.
Also, latin used it until 17. Why the ending of latin was changed for the spanish/french for ten for 17 or 16 and 17 is anyone guess. Maybe “seisse” or “septze” sounded funny and were difficult to pronounce, simply.
Tiny nitpick to your very comprehensive post: 20th of the month is hatsuka. The word misoka also deserves a mention; literally meaning 30th day, it’s now used to refer to the last day of the month (and o-misoka for the last day of the year).
I have always wondered why Italian teens start out one way and then flip around the other way.
11 undici
12 dodici
13 tredici
14 quattordici
15 quindici
16 seidici
All well and good so far: first the units value, then the ending derived from the Latin word for 10. But:
17 diciassette
18 diciotto
19 diciannove
(Everybody already knows venti is 20, right?) What are 17, 18, and 19 doing flipped? In the original Latin, septendecim for 17 isn’t flipped. However, 18 is duodeviginti - which literally means ‘two down from twenty’ - and 19 is undeviginti ‘one down from twenty’, so Italian formed those last two teens all on its own with no help from Latin.
P.S. At home our big coffee mugs hold a whole pint. I say I’m having a “seidici.”
Given that it works that way for several Romance languages (at least French, Spanish, Catalan, Italian and Portuguese; Romanian is different), I suspect the vulgar Latin has worked that way… maybe not since the times of the Republic, but definitely by the time the Western Empire fell.
Correction: three head of cattle, not three heads. At least, not in my dialect. (Same with “stone” as a unit of 14 pounds: I weigh twelve stone (I wish!), not twelve stones.)