The words "nineteen-hundreds" to me mean strictly 1900–1909. I've noticed several times that people, invariably North American, use these words to mean "the twentieth century", or 1900–1999, or something like that. Similarly for "the eighteen hundreds" used to mean "the nineteenth century" and so on.
Is this an example of a misuse of words by people who have heard and then misunderstood them, or is this actually an established usage in America? Secondly, if it is not a misuse, how would said Americans refer to the period of 1900–1909?