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The extra day inserted into a leap year is actually February 24th. The old 24th of February becomes the 25th, etc, with 28th February become the 29th February.
This is because Julius Caeser's calendar reform (which is still the basis (with a minor tweak) of our current calendar) said that in leap years the "6th day before Kalendae of March" should be doubled. That is to say, there should be an extra February 24th. This matched the position of the leap month, Intercalaris, of the pre-Julian Roman calendar.
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