As we start the new decade . . . WAIT, STOP THE PRESSES!
I’m enjoying heading into this century’s version of ‘The Roaring ‘20s’ as much as anyone, but just to be clear:  NUMERICALLY, at least, we don’t really start the new decade until 2021. 
I feel like I’m swimming into deep water here, and I’m braced for the chorus of boos that may erupt. Indeed, perhaps I’m slowly turning this molehill into a small mountain.  Nonetheless, it’s true:  Numerically, at least, we don’t start our new decade until Jan 1, 2021.  Worse yet, we didn’t start the 21^st century until 2001.
Let’s have a little bit of harmless fun here: Suppose you have a stack of 100 pennies that you wish to turn into 10 dimes, after which you want to turn the 10 dimes into a dollar.
The change-making teller requires accuracy, of course, so he/she will not actually give you your first dime until you’ve given him/her your TENTH penny, namely Penny #10.  Now, with one dime in hand, you will begin counting out your next set of pennies with Penny #11 (not #10), moving toward your second dime.  Before long, you’ll be ready to cash in your ten dimes for a dollar, but the teller still won’t trade you for the dollar until you’ve given him/her your TENTH and final dime, which, in turn was received when you turned in Penny #100. 
So, now, with your dollar in hand, you are finished.  But if you choose to repeat this cashing-in process toward another dollar, you will start it with Penny #101.  (Not Penny 100 – you don’t have it anymore, remember?)
You already see the picture.  In the tedious exercise(s) above, please feel free to substitute the word ‘year’ for every ‘penny’, the word ‘decade’ for every ‘dime’, and ‘century’ for every ‘dollar’.  Then read it back to yourself and see what you think.
This parallel works so well precisely because we always begin counting things at 1, and not 0.  On the other hand, if you wish to go back 2000 years and decide there was (or that calendar makers later put) a Year 0 between the BC/BCE and AD/CE sets of years, that would be another story, but most scholars don’t do that.  Neither did the Roman monk who designed our current system in 525 AD. (Thanks, Google!)
Naturally, nothing here is of earth-shaking importance.  As I say, I look forward to the ‘20s, which I’ll carefully agree we’re entering.  And I have no problem with calling them that.  It’s a matter of perspective.  I hope we will all enjoy (and live through!) them – and that they are much less stressful politically than the ‘10s. (‘teens’?)
But if we want to be precise with the calendar – and with our base-10 numeration system – we will also keep in the back of our minds that we are only 19 years into our century, having just begun the 20^th, and that our next numerical decade begins a year from now. 
Whatever your decade preferences, I wish you a Happy New Year!