"Late 1900s" = 1909 "Late 1930s" = 1939 "Late 1990s" = 1999 No?

Speaking as a historian, yes!

It's not for us to police how young people use language.

i see it as like saying 1877 is the "late 1800s" which makes sense to me?

Yes, what they should say is late 20th century

Ouch

Exactly

Yep. When did people start referring to a century by stating xx00s? That's pretty sloppy and loose describing a century.

To my mind, 1900s refers to 1900-1999, but the decade from 1900 to 1909 may be called the 19-aughts.