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We have a leap year because it takes 365.25 days for the Earth to make one orbit of the sun. As we do not count quarter days in the calender, every 4 years we get 1 day so we add it to February and make it 29th of Feb a leap year.

That's the short answer. The longer answer is that it takes very slightly more than 365.25 days (365.256363004 days, an error of about 9 minutes a year) for the Earth to revolve around the Sun. Using the rule of every fourth year being a leap year, this adds up to an error of about 3 days (2.545 days) in 400 years, so the full rule is that every year evenly divisible by 4 is a leap year, except that century years not evenly divided by 400 are not leap years. Example, 2000 was a leap year, but 2100, 2200, and 2300 will not be leap years.

This system, the Gregorian Calendar, was put into place in 1582 by Pope Gregory XIII in order to correct for the prior Julian Calendar, which assumed 365.25 exactly. The change also included dropping the ten extra days that had accumulated, realigning the Vernal Equinox with March 21st, and it adjusted the Lunar Calendar as well, because it was off by about 4 days at that time.

It is interesting to note that these observations and calculation were made in the 16th century, using (by today's standards) not very accurate measurements. It is also interesting to note that England did not fully agree with this, due to the dichotomy between the Roman Catholic Church and the Church of England, so they kept the leap years for 1700, 1800, and 1900, stepping into alignment in 1923.

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