Nowhere. But the English sentence needs it in the way the English translation is constructed. If you instead said "I'm writing the century's book" it'd be a grammatically correct sentence, and "book" not being definite for the same reason.
I was confused at first by this too but then I realized it is like "Jag tycker om flickans bok." which would be translated as "I like the girl's book.", or "the book of the girl", yes?
The slow version is very misleading imho. Usually the slow version makes it very clear where one word ends and another begins, but in this case it sounds just like: Jag skriver århundrade (t)sbok. There's a clear pause between århundrade and tsbok.
No-one's fault of course, but very confusing if you rely on the slow version.
Sounded fine to me, but maybe it's because I know the word 'århundradets' so I didn't attach it to 'bok'. I encountered 'århundrade' several questions before this one, so I easily distinguished it, I guess.
How would one write, "I am writing a book on the century" (referring to a century already mentioned)? How would one write "I am writing a book on this century"?
Tack! This seems similar to an American regional construction, "this here" as in "I am feeding this here dog". I think this will help me remember it. I got such insight into the origins of my language learning French and now Swedish is "taking me to school" all over again! What an unexpected pleasure!
Because it's the definite form. ett århundrade, århundradet, and it's 'the book of the century'.
Is this supposed to be the best book of the century or am I just writing a book about a certain century?
Definitely the former. The latter would probably be using om ("about") somehow.
English can use either "the y of x" or "the x's y". Swedish can use only the latter. But boken århundradets would use "the y the x's" which doesn't work in either language.