If you want to be technical about it, Washington was actually born on February 11, 1731, not on February 22, 1732. When he was born, England and its colonies followed the Julian calendar, which was instituted in 46 B.C. by Julius Caesar. So, by that calendar, Washington was born on February 11, 1731. In 1752, England switched to the Gregorian calendar, which is still used today. It’s according to that calendar that he was born February 22, 1732.
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Washington actually preferred this original date of February 22nd, and his birthday is still celebrated today.