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Because nothing is "zeroth" in the numerical order, there is no "year zero" in either the Gregorian calendar or the Julian calendar). The first decade of the Common era runs from the beginning of the year 1 AD through the end of the year 10 AD, while the decade before it starts at the beginning of the year 10 BC and ends at the end of the year 1 BC.
The years 1 BC and 1 AD are consecutive, and so are the 1st century BC and the 1st century AD. Note that the term "the year 1" means "the 1st year", because the English uses cardinal numbers for years, instead of the more complicated ordinal numbers. This usage may not be relevant when the number of the year is small, but does come into prominence with three or four-digit numbers.