There is no year 0. The historical calendar goes directly from December 31, 1 BC to January 1, AD 1. As such, the non-existent year cannot be part of any decade—ordinal or cardinal—and the 0s only have nine years in them.
Years were historically measured by the years of the ruler. It would be "the first year of King Bob's rule", then "the second year of King Bob's rule", and so on until the ruler died, at which point they would start the same again with the next ruler. This worked, but having such short calendar eras made going back hundreds of years require lots of of history research and addition.
Then in the year 525, Dionysius Exiguus, a Scythian Christian monk, was calculating and listing all the dates on which Easter would fall for the next hundred years. Justin I was emperor, but obviously would not be for the next hundred years. Eastern Christians had been making such lists since Diocletian, and so to simplify things, they had just continued using the years of the Diocletian era. However, Dionysius did not wish to continue using Diocletian's inauguration to number years because Diocletian had been a tyrannical emperor who implemented the largest and bloodiest persecution of Christians in the Roman Empire's history. So Dionysius numbered his years off when he thought Christ was born, as Christians believe that Christ is king forever and Christ's birth was when he came to earth. Dionysius's new "anno Domini", or "in the year of our Lord" calendar era caught on across the Christian world and became the planet's de facto calendar system.
However, the AD system did not account for years before Christ. Eventually in the late middle ages, "BC" caught on as the complementary way to refer to years before Christ. As a way of measuring before Christ as opposed to after Christ, it made sense to again start at 1 BC, and so neither era has a year zero.