Did people in the late 19th century and early 20th century refer to the decades in the 1800's as the 20's,40's..ect as we do today about the 1900's?

by mbeaumont1
Monkeyavelli

Yes. Here's an except from the Pulitzer Prize-winning novel The Magnificent Ambersons by Booth Tarkington, published in 1918 but set in the 1870s-1910s. This is from the very beginning where the author is taking a (remarkably modern-sounding) wry look at changing fashions since the 1870s:

In the early 'eighties, while bangs and bustles were having their way with women, that variation of dandy known as the "dude" was invented: he wore trousers as tight as stockings, dagger-pointed shoes, a spoon "Derby," a single-breasted coat called a "Chesterfield," with short flaring skirts, a torturing cylindrical collar, laundered to a polish and three inches high, while his other neckgear might be a heavy, puffed cravat or a tiny bow fit for a doll's braids.

The term the Gay Nineties was also used in the US starting in the 1920s to refer to the 1890s.