A decade (or a century, or a millennium) begins whenever you say it does, as long as it ends a decade (century, millennium) later. The problem is people equating two different decades (centuries, millennia) that are defined slightly differently.
The 1900's obviously began on Jan. 1, 1900, and ended on Dec. 31, 1999.
The 20th century began on Jan. 1, 1901 and ended on Dec. 31, 2000. It had a 99-year overlap with the 1900's, but it's not quite the same thing.
And likewise with decades: the 00's began on Jan. 1, 2000, and ended on Dec. 31, 2009, while the first decade of the 21st century began on Jan. 1, 2001 and will end on Dec. 31, 2010.
It doesn't work quite the same way with people's ages, since people aren't born at age 1: when you turned 30, you simultaneously entered your thirties, your fourth decade, and your 31st year.
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The 1900's obviously began on Jan. 1, 1900, and ended on Dec. 31, 1999.
The 20th century began on Jan. 1, 1901 and ended on Dec. 31, 2000. It had a 99-year overlap with the 1900's, but it's not quite the same thing.
And likewise with decades: the 00's began on Jan. 1, 2000, and ended on Dec. 31, 2009, while the first decade of the 21st century began on Jan. 1, 2001 and will end on Dec. 31, 2010.
It doesn't work quite the same way with people's ages, since people aren't born at age 1: when you turned 30, you simultaneously entered your thirties, your fourth decade, and your 31st year.
pedantically...