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Adolescence as a separate stage of development was not considered until the twentieth century.
Twentieth Century
Twentieth.
"A twentieth" / "one twentieth" or "the twentieth" (depending on the context).
The plural is twentieths.
No. Numbers in a normal sentence are not capitalized.
Example: "My birthday is on the twentieth of January."
Twentieth does not have a prefix. Just simple numbers do not usually have a prefix.