"Friday is the fifth day of the week."
Translation:Piątek to piąty dzień tygodnia.
So when using the cardinal numbers to quantify nouns, they take the genitive but when using ordinal numbers with nouns, do they always take the nominative?
An 'ordinal number with a noun' creates a noun phrase, which has to behave like any other noun phrase and take the appropriate case. You have an "X is Y" sentence here, and as you know, there are two ways to write that in Polish.
"Piątek to piąty dzień tygodnia" puts the noun phrase "the fifth day of the week" in Nominative, but it can also be in Instrumental if you use the 'jest' construction: "Piątek jest piątym dniem tygodnia".
A cardinal number + a noun generally does the same. "I see five books" is "Widzę pięć książek" (the noun phrase 'five books' takes Acusative), but "I need five books" is "Potrzebuję pięciu książek" (it takes Genitive now).
As for 'what case does the numeral itself take', most of them take Genitive (pięć książek), but some of them (1, 2, 3, 4 and those ending with -dwa, -trzy, -cztery) take Nominative (trzy książki).
Ordinal numbers behave like adjectives.
Hey, Jellei: I know I'm not the first to say it, but thanks so much for the work you put in here clarifying and explaining things. This course is easily 10x better thanks to your input.