1810s (or 1810's), 1820s, is perfectly clear, but 1800s covers the entire century for Americans and Canadians.
People not used to thinking in time terms often click (in their minds) on 1800-1899 if you say 18th century, then re-think ("Oh, how silly of me!").
This is one that was missed in the language threads.

Department of strange associations. This song reminded me of the country tear-jerker- "You picked a fine time to leave me, Lucille. Six hungry children and a crop in the field."