It's just math, really. Year "one" covers everything from the smallest fraction you can devise of past "0" and only really completes its year the imperceptible moment that signals the transition from 1 to 2. Think .999999 and 1, except for the sake of things being easy 1 represented that fractional number the whole year (so that we can say it is 1983 instead of 1982 67/365) and so "2" picks up the moment you actually finally complete "1" but have only made the smallest possible progress into "2".... lol
To put that in century terms, when it hits "100" you're really only, say, 99 1/365 through the century.