Your math is correct. There are not exactly 52 weeks per year, it is only an approximation. All the calendar systems, including our Gregorian calendar, have had to adjust out some inaccuracies of fitting our traditional use of a week to the solar cycle, and some are better than others.

According to Wikipedia, "In a Gregorian mean year there are exactly 365.2425 days, and thus exactly 52.1775 weeks" The Julian calendar that was previously used had "365.25 days or 52

In both systems, there are about ~0.25 days extra per year, which accounts for the extra day in February during a leap year.

Even after observing leap years, there are also leap seconds they occasionally have to adjust out because of the Earth's orbital decay and tidal forces. See en.wikipedia.org

According to Wikipedia, "In a Gregorian mean year there are exactly 365.2425 days, and thus exactly 52.1775 weeks" The Julian calendar that was previously used had "365.25 days or 52

^{5}⁄_{28}weeks." And once you understand there is no modulo relationship of a week to a year, then it makes sense why our months (and years) end up starting on a different days of the week.In both systems, there are about ~0.25 days extra per year, which accounts for the extra day in February during a leap year.

Even after observing leap years, there are also leap seconds they occasionally have to adjust out because of the Earth's orbital decay and tidal forces. See en.wikipedia.org