Why are the dates of some events in history given approximately?

This is due to the peculiarities of science and methods of its study. If we are talking about rather ancient times, then most often the dates are determined on the basis of examinations of objects, which, albeit quite accurate, but sometimes cannot perfectly accurately determine the age of a thing, therefore the date will be approximate. If we talk about later stages, for example, the early Middle Ages, when written sources become the main way of knowing history, then the inaccuracy in determining the dates is associated with discrepancies in the chronicles of different authors.