Exact science refers to systematized knowledge. So that predictions, and their verification, are possible, by measurement, experiment, observation, and rigorous logical argument. Or at least, more realistically, so that predictions undergo this kind of testing, and may eventually get rejected, if it becomes agreed that they do not satisfy the tests.
Mathematics, the natural sciences, and the applied sciences are considered exact. It is essential that their results and hypotheses be public, so that repeated testing and development is a universal endeavor. For this reason, it can be said that exact science, at least in the strict sense, did not arise until the invention of the publicly available scientific journal, say around 1640, or at least with the availability of printed books, say around 1540, in Europe. This does not necessarily imply that results before that time were invalid. But many are seen that way today, in the light of the intense scrutiny that characterizes todays exact sciences. This relentless testing, and the ensuing error-correction, so to speak, translates into the very high degree of reliability of the established results in these sciences.
Exact sciences are distinguished from the social sciences on the one hand, and from the humanities, theology, the arts on the other. Nevertheless, some fields of study, such as for example economics, may share some of the features characteristic of the exact sciences. The primary distinction lies in whether experimentation is feasible (or indeed advisable), and whether experiments can be designed so that they provide reproducible evidence. As distinct from so-called anecdotal evidence, obtained from a single observation only. In this respect, astronomy is hard put to qualify as an exact science, precisely for the lack of experimentation. However, there are huge numbers of stars to be observed, in (almost) all relevant stages of the stellar life cycle, and this provides almost as reproducible data as experiments otherwise do.
See also