Hi @Germanlady, good question!
Numbers are called “Numerale” in German, and (depending on which linguistic school you’re following) can be described as adjectives.
In both examples, the numbers are attributes of a noun, but in the first sentence “Euro” is plural, and we don’t use an article when it comes to indefinite articles in plural.
If a room for a night would be exceptionally cheap and you could spend the night for just one Euro at the hotel, one, or a Euro would be “ein Euro” which would be the indefinite singular article for “der Euro”. But with multiple Euros, we use something called “Nullartikel”, which is basically no article at all.
- Ich esse heute eine Kartoffel zu Mittag.- Ich esse Kartoffeln zu Mittag.
- Das Zimmer kostet ein Euro pro Nacht. - Das Zimmer kostet 82 Euro pro Nacht.
In the second sentence we have the declined article (Akkusativ) of “der siebzehnte” - but the seventeenth of what? Der siebzehnte Dezember zum Beispiel!
So the accusative article "den" is connected to the (implied, but not specifically mentioned) month. The number “Siebzehn” is just used as a numeral to specify which day of the month we are talking about - “den” is the article of the noun, not the article of the number.
PS: The plural of “Euro” is “Euros”, but when we used it with numerals larger than one it’s always “Euro”.