The correct answer is option 3: The length of a year is not an integer number of days.

The Earth takes approximately 365.24 days to orbit the sun. However, our calendar system is based on a year consisting of exactly 365 days. This means there is an extra 0.24 days that are not accounted for in our calendar.

To compensate for this discrepancy, we add an extra day to the calendar every four years, creating a leap year. This additional day, known as February 29th, brings the total number of days in that year to 366 instead of the usual 365.

This adjustment helps to keep our calendar year synchronized with the actual time it takes for the Earth to orbit the sun. Without the leap year system, our calendar would gradually drift out of synchronization with the astronomical year, causing the seasons to occur at the wrong times.

So, it is necessary to have a leap year every four years in order to account for the fraction of a day that is not included in our standard 365-day calendar year.