Exactly. And note that we much more naturally delineate the decades such as the 80s, 90s, 00s, etc. Nobody in ordinary contexts refers to the 210th decade, which of course doesn't start for another year.
With centuries we tend to think of them as the 19th, 20th, 21st centuries much more naturally, which leads to confusion, because these don't correspond to the 1800s, 1900s, 2000s.
1900 is the first year the 1900s, while it is the last year of the 19th century. 1901 begins the twentieth century, but it is the second years of the 1900s.
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