You may recall the endless debates about whether the New Century began on January 1, 2000 or January 1, 2001. (I tried to argue with friends that it wouldn't occur until the year 5800, which wouldn't occur until 2040, but they didn't listen to me.)
The whole question revolved around whether or not there was a "Year Zero." And obviously, with respect to the Christian/Gregorian Calendar, there wasn't. So, the argument went, the "21st Century" began on January 1, 2001.
However, as I liked to point out -- a new century begins every second. Some centuries are just more popular than others. The same applies for decades, and years.
"The 1900s" began on Jan 1, 1900, and ended Dec 31, 1999. It seems logical to me to define "The 1900s" as any four-digit year beginning with the digits '19'. "The 2000s" would be defined similarly.
What about Decades?
No one referred to the past decade as "The 201st Decade." If we referred to decades as such, the 202nd Decade would begin on January 1, 2011. But we don't. The 2010s begin on January 1, 2010. It doesn't make any sense (to me) to look at it in any other way.
Wikipedia may be helpful if you are confused.