How many days are there in a century?

Question

How many days are in the century running from 1 January 2001 to 31 December 2100, inclusive? Then compare with the previous century, 1 January 1901 to 31 December 2000. Are the two counts the same? If not, which one is longer and why? A hint before you begin: "one hundred years" is not one fixed number of days.

Accepted Answer

36,524 days for 2001 to 2100. The 1901 to 2000 century has 36,525. Base count. 100 years × 365 days = 36,500. Add one day per leap year. Leap years 2001 to 2100. Years divisible by 4 in this range: 2004, 2008, ..., 2100, which is 25 years. But 2100 is divisible by 100 and not by 400, so it is not a leap year. That leaves 24 leap years. Total: 36,500 + 24 = 36,524. Leap years 1901 to 2000. Years divisible by 4: 1904, ..., 2000, again 25. This time the century year, 2000, is divisible by 400, so it stays a leap year. All 25 count. Total: 36,500 + 25 = 36,525. So the two centuries differ by one …

How many days are there in a century?

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