"Ten is a tenth of one hundred."
Translation:Dek estas dekono de cent.
Update: For anyone who is also confused by this, I have learned the answer. Da is never used when discussing numerals, e.g. cent, tridek, dekono.
Why is 'unu cent' incorrect? Is there no difference between a hundred and one hundred?
No; in English, they are synonymous, and in Esperanto, we don't say "unu dek" or "unu cent", and usually not "unu mil" either: http://bertilow.com/pmeg/gramatiko/nombroj/vortetoj/formoj.html
What do you mean "as if they were nouns"?
Fractions are nouns.
You can say "a fifth", "the third", "my quarter of the cake", "the blue half and the green half" just as you can say "a book; the book; my book; the blue book and the green book".