Additional Math Pages & Resources

Monday, February 29, 2016

Leap Year Math

Perhaps you've heard that this year 2016 is a leap year. How do we know that?

We use the figure 365 for the number of days in a year.

In actuality, the number is closer to 365.25. To compensate for this discrepancy, every four years we have what is called leap year.

In leap years, a day is added to February. Normally February has 28 days.

However, every 4 years, we give February 29 days to  help synchronize the calendar year with the solar year, or the length of time it takes the earth to complete its orbit about the sun,  about 365.25 days.

A leap year has 366 days. The year 2016 is a leap year with 366 days. So the month of February will have 29 days.

Because 365.25 is not exact, three leap years are dropped every 400 years.

These are the end-of-century years that are not evenly divisible by 400.

These rules only apply to the Gregorian calendar currently used by American and European countries.

Several other calendars are used by Asian countries.

Here's a formula we can use to find out if a year will be a Leap Year:

Leap Years are any year that can be evenly divided by 4 (such as 2012, 2016, etc.)

   except if it can can be evenly divided by 100, then it may not be (such as 2100, 2200, etc.)

   except if it can be evenly divided by 400, then it is (such as 2000, 2400, etc.)

In other words:
1. Divide the year by 4. If there is no remainder (so it divides evenly), it may be a leap year.
2. Divide the year by 100. If there is no remainder, then it may NOT be a leap year.
3. Divide the year again, by 400. If there is no remainder, it is a leap year.

Both 1600 and 1700 are evenly divisible by 4. However, 1700 was not a leap year because 1700 is not evenly divisible by 400.

Can you determine which of these years were leap years? The answers appear below.

             1960            1930             1836              1862

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1960 and 1836 are both divisible by 4 and 400. 1960 is also divisible by 100. So both 1960 and 1836 are leap years.

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