Hope this explaination helps

The first year AD is known as year 1. Too bad, because that’s been confusing people since. Year 1 is the first year, so how many years AD were before year one? Zero. By labeling the first AD year “1”, you are counting not how many years have already passed, but what year is currently passing. So the year 100 AD is still in the first century because 100 years have not passed until the end of year 100. If we had started with year 0, then year 99 would have been the last year in the century and 100 would be the first year in the 2nd century.

The same situation is there for the centuries. Year 1 AD was in the 1st century, not century zero. So, the first century was years 1 through 100. The second century was years 101 through 200. The third century was year 201 through 300, and so on. You can see how this is somewhat confusing. If you keep labeling the years/centuries this way you can see that the year 1999 was not, in fact, the last year of the century. 2000 was the last year of the century. So all of that partying to celebrate the end of a millinium on 12/31/99 was an entire year early. The powers that be certainly knew this and decided that this was just too much for the average person to handle. So, for whatever reason, people were generally convinced that 1/1/2000 was a new century, and perhaps not wanting to be a party pooper, no one made much of an issue about it. Or maybe it was that Prince song, who knows? Subsequently, 1/1/2001 came and the fact that this was the beginning of a new century was pretty much missed.

I partied on both dates – the true sign of an intellectual!