Many (but not all) people consider the apostrophe unnecessary when the number is in the double digits and above. Most authors presently prefer the 1900s, although others prefer the 1800s. If you use numbers to identify decades, the '30s are the most common, but you'll also see the '30s and, on rare occasions, the '30s. There are only 100 years in the 20th century, so they are always written as two words. You should use the 1900s because it is a widely accepted style guide rule that when writing about periods, you should use the last year of that period as your own beginning point. So if you want to be accurate, you'd use 1999 instead of 2009. The 2000s began in 2000 and will end in 2100. The 21st century began with the arrival of the new millennium and will end after 4,000 days (which is approximately three years). Using these definitions, I calculated that the 2000s begin in January 2001 and end in December 2020. The one disadvantage to using this style is that it may not be familiar or comfortable to some readers. In general, writers tend to avoid using the word century to describe any period shorter than 100 years. The only other option is to use the 1810s, but this is less common. The 19th century began in 1810 and ended in 1910. This is because before 1971, the year was only counted forward by 10 instead of 100.