and the 2000's ?

Hola Alan

There is no specific rule for these. If referring to the first decade of 2000 (2001 - 2010) we would probably say "la primera década del 2000"; for the second decade (2011 - 2020) you can say "la segunda década del 2000" or "la década de los diez". But if you use this last one it may not be clear if you refer to this century or the previous one, i.e. 1911-1920; so in these cases we clarify as much as possible and the best way is to use "la primera década de...", "la segunda década de..."

Saludos

Inma