It’s the same in a lot of the other languages mentioned.
Másfél = más (more, yet, another) + fél (half)
Anderhalf/anderthalb: another half
I’m not sure what the deal with Polish półtora is. Pół is “half,” but I don’t know what the ending could mean.
German doesn’t really count, though, does it? That word means one-one-half, it’s not a separate word, but an agglomeration of words. If that counts, then German has a “word” for every number.
The Slavic languages generally derive the numeral “one and a half” from the Proto-Slavic *polъ vъtora, which roughly translates as “half of the second”. In Old Polish (and other older variants of Slavic languages) you can also see forms such as półtrzecia < *polъ tretьja “two and a half” (literally, “half of the third”).
The numeral still behaves like a compound, rather than a single, word. The genitive of “1.5” in Russian, for example, is полутора – both components take genitive endings. This is true for other numerals above ten, at least in Russian.
(Thank goodness for Serbian, which dispenses with declining numerals! Makes life much easier.)
Aha! That makes sense. The Polish word for Tuesday is “wtorek,” which I understand is related to an old word meaning “second” (as in “second day of the week.”) Looking at your transcription of the Proto-Slavic, I see the connection now.
“anderthalb” counts. It’s a special word meaning “one and a half”, not an agglomeration of words.
I can add Lithuanian “pusantro” (one and a half) and for that matter “pustrečio” (two and a half).
I was responding to Mops, who used eineinhalb (which Google translated as one and a half). Anderthalb looks like it means “another half”, but Google translated it as “half”, although that’s clearly wrong.
In any case, German makes new words out of all of its numbers, doesn’t it? One thousand nine hundred is einstausendneunhundert. How many languages have a word for that? 
Uh, uh, I know this one:
Danish: Halvanden.
Greek: μιάμιση.
This is correct.
I am not sure what you mean by “agglomeration” of words? Words are formed by various means and a major one, especially in German, is Komposition, the compounding of primary words.
There are special cases, the so called “Zusammenrückungen” (amalgamations) that don’t fit into the types that are mostly used to distinguish the various means of compounding words in German; examples are expressive words like “Dreikäsehoch” (“three-cheeses-high”, which could be translated with nipper) or “Taugenichts” (a good-for-nothing).
There are also words called “Autokomposita” or “Iterativkomposita” that form a word by a kind of iteration, like “Schickimicki” (a derogatory word for the in-crowd) or “Wirrwarr” (clutter); such words tend to annoy linguists who prefer clean structures and hard rules.
Anyway, numerals are perfectly fine words in German; One Thousand and One Nights is in German “Tausendundeine Nacht” and “hundertundein Auto” is a grammatically correct way to talk about one hundred and one cars.
Einundeinhalb or eineinhalb or anderthalb mean almost the same thing though there is a miniscule difference in meant precision (anderthalb does not necessarily mean 1 ½ precisely but something in the ball-park).
The “ander” part of the word comes from an older use of “andere” (another) – it used to refer to “the second one”, which means that the word should be translated into modern German with “zweithalb” (one and the half of another one), but that way of talking about figures is outdated and nowadays mostly used in dialects.
The OP said that only one language has a word for 1 and a half. That’s clearly wrong, given the multiple examples above. However, my point was that German sort of doesn’t count, since that language just jams together number words to form new numbers. How many languages have a word for one thousand nine hundred? One thousand eight hundred? One thousand seven hundred? Two thousand? etc.
Eineinhalb seems like a similar word – one one half. Anderthalb also seems similar – another half. So, you could say that German has a special word for one and a half, but when you think about it, it’s not all that special – German has a special word for many many numbers.
That’s all I meant when I wrote that German, in some sense, doesn’t count. It doesn’t have a new or special word for one and a half, it combines multiple words to create that word.
Let’s say that many languages didn’t have a word for two, but instead used (in English, for example) one and one. Now, someone states that some other language has a special word for two. Someone else jumps in and says that German also has a special word for two.
If that word is zwei, then, yes, I agree that counts. If that word is einundein or einein or something, then not so much.
In any case, it looks like the tour guide was pretty mistaken about the specialness of that Hindi word.
Given that the OP did not raise any limits on how those words originate, but only ask whether they exist, I disagree: the German words are single words, and therefore perfectly valid.
Ettusenniohundra in Swedish.
I did not indeed give any limits on those words. The tour guide might have, but he’s not a Doper, so we don’t care about him. 
The funny thing is too, he’s white so it’s not as though he was extolling how wonderful hindi was compared to the rest of the world. I mena, maybe he was, but not because it was his own cultural linguistic pride - I think he’s Finnish or something.
Fascinating, btw - I have often complained that for all that English steals words ruthlessly from other languages, we still should steal more words. We also have a word for '2.5" - “dhai”. At 3.5 We have to go back to saying “three-and-a-half” or “sade-theen”.
Off-topic, I was really looking forward to the tour of Dehi - it was written in the 2000s I believe so I figured it would be an up-to-date look at a city I haven’t seen in almost twenty years. And it was…but I could not read very much of it because the man apparently was only alloted one paragraph break per chapter. I cannot read solid walls of rambling text.
Yes. 
I think, I see what you mean. But (who didn’t see a but coming?) from the point of view of word formation, oneone would be as much a distinct word as two is (or eleven), only the means of its creation were different. Or is sixteen less of a self-sufficient word because it’s a compound of six and ten?
Germanic languages show a tendency to form new words from known ones by “smashing” them together; it’s not as often or as quickly done in English as in German or Swedish but still common: the mailman is the Briefträger (letter carrier), for example. And though you write driver’s license or driver license, you could compose the word driverlicense too – which would then be almost identical to “Führerschein” .. still, you could not make the same pun: “Der Führer war ein armes Schwein, er hatte keinen Führerschein.” (the Führer [aka Hitler] was a poor devil, he had no driver’s license .. Sigh, not funny at all in English, not even a little bit – no rhyme either; the limits of translation when it comes to connotation).
Anyway, whether you invent a word from thin air or compose one from known ones, the result is a new word and if it is added to the active vocabulary of the public, it will change over time. And a compounded word might at some point in the future seem like a special word, like eleven, even though such a word can be traced back to ain-lif (according to some theories). More seemingly unique words [del]are[/del] were compounds once than you might think, even in English.
Btw, I think the capitalisation of nouns in German is one major reason for our willingness to form new words with older ones, even if the result is a pretty long word - the first capital letter works like a beacon that helps to identify the structure of a sentence with one glimpse: you know the position of the entities involved immediately and only have to find out their relationship.
I guess I should not have said that it doesn’t count, it’s just less interesting than other cases where there really is a new and different word that means 3/2, even if that new and different word evolved from some root that meant 3/2.
Oh well, back to the scheduled thread topic.
How do you say “second” in Polish now, then? In Bulgarian, it’s vtori, and the connection with Tuesday (“vtornik”) is obvious.
BTW, Bulgarian does not have, AFAIK, a single word for “one and a half”, or at least one that anyone uses with regularity.
I’ve always been fond of the English phrase “half again”, as in “half again as large.” Surprised that hasn’t gotten a mention here yet.
Yes, yes, I know you’re looking for single words. But honestly the distinction between simple words, compound words, hyphenated phrases and just plain phrases tends to be academic, and it seems to me the vast majority of interesting words start at the multi-word end of that spectrum and then drift inexorably toward the other as they get used more and more, without ever having a significant change in meaning.
Gujarati has specific words for .25, .5, .75, 1.5 and 2.5