999 is the final year of the 10th century
1000 is the first year of the 11th century.
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10th century.
The 20th century. We add 1 to the first two digits to get the century. This is since the first century is classed as the years 0 to 999, the 2nd century the years 1000 to 1999 etc.
The 11th century 0-99 is 1st century 100-199 2nd century 200-299 3rd century .. .. .. .. 900-999 10th century 1000-1099 11th century .. .. .. .. 1900-1999 20th century 2000-2099 21st century
The years 0 to the end of 999 are the 'first century'. Counting up from there, 1350 is in the '14th Century'.
You could theoretically be 999 999 002 009 or 999 999 002 010 years old; however, because the universe is nowhere near that old, it is preposterous to ask how old one would be given a birthday in a year that never existed.