You would not hear the phrase, "in the 1900's", with the meaning of, "in the years from 1900 to 1999." The phrase, "in the 1900's," means, "in the years from 1900 to 1909." If you mean "in the years from 1900 to 1999," you'd say "in the 20th century." (However, the phrase "in the 1800's" means "in the years from 1800 to 1899." "In the 1700's" means "in the years from 1700 to 1799." Etc.) The