Does "nineteen-hundreds" refer to 1900–1909 or 1900–1999?

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?

Although people do use it mean 1900–1909, it isn't a misuse to use it to mean 1900–1999. Another way to refer to the first decade would be "just after the turn of the century", or "at the turn of the century". I would say 1920s to mean 1920–1929 though.

If you do a corpus query (COCA) you'll find that 1900s is almost always preceded by early. (121 times out of 149 hits). This qualification leads me to think that most authors think that the 1900s is a large time frame, that benefits from further qualification. Furthermore, in many cases the context shows that "early 1900s" refers to years outside of 1900–1909.

I think of any "hundreds" term as representing the entire century and depending on the specificity demanded in the situation use "early nineteen hundreds" or "late nineteen hundreds" to reference a period. When referring to the first decade of the twentieth century I might say "the nineteen aughts," perhaps a little pretentious , but I like the sound of it.

It's worth noting, though, that I rarely hear "nineteen hundreds" used to refer to anything later than the earliest portion of the century, perhaps because it's so recent and most people can still remember portions of the latter decades. I hear "eighteen hundreds" much more commonly used to refer to that entire century.

I've never known "nineteen hundreds" to mean anything but the 20th century. I come from a Computer Science background, so I understand why logically it would seem to be "nineteen hundreds" --> 1900-1909, "nineteen hundred and tens" --> 1910-1919, etc., but I haven't heard it used to refer only to 1900-1909.

As to how to refer to that particular period... what about nineteen-ohs? Like "twenties, tens, ohs..."

In the US at least, there's enough variation in the use of this term as to render it imprecise to the point of being useless.