why is that 1896 was a leap year but not 1900?

Question

why is the first year of every century divided by 400 to check for a new year?

Answer 1

The Rule
According to the Gregorian calendar, which is the civil calendar in use today, years evenly divisible by 4 are leap years, with the exception of centurial years that are not evenly divisible by 400. Therefore, the years 1700, 1800, 1900 and 2100 are not leap years, but 1600, 2000, and 2400 are leap years.

Background

The Gregorian calendar year is intended to be of the same length as the cycle of the seasons. However, the cycle of the seasons, technically known as the tropical year, is approximately 365.2422 days. Since a calendar year consists of an integral number of whole days, a calendar year cannot exactly match the tropical year. If the calendar year always consisted of 365 days, it would be short of the tropical year by about 0.2422 days every year. Over a century, the calendar and the seasons would depart by about 24 days, so that the beginning of spring in the northern hemisphere would shift from March 20 to April 13.

To synchronize the calendar and tropical years, leap days are periodically added to the calendar, forming leap years. If a leap day is added every fourth year, the average length of the calendar year is 365.25 days. This was the basis of the Julian calendar, introduced by Julius Caesar in 46 B.C. In this case the calendar year is longer than the tropical year by about 0.0078 days. Over a century this difference accumulates to a little over three quarters of a day. From the time of Julius Caesar to thesixteenth century A.D., the beginning of spring shifted from March 23 to March 11.

When Pope Gregory XIII instituted the Gregorian calendar in 1582, the calendar was shifted to make the beginning of spring fall on March 21 and a new system of leap days was introduced. Instead of intercalating a leap day every fourth year, 97 leap days would be introduced every 400 years, according to the rule given above. Thus, the average Gregorian calendar year is 365.2425 days in length. This agrees to within a half a minute of the length of the tropical year. It will take about 3300 years before the Gregorian calendar is as much as one day out of step with the seasons.

God Bless You and Our Southern People.

Answer 2

Rules for Determining a Leap Year
1. Most years that can be divided evenly by 4 are leap years.
(For example, 2004 divided by 4 = 501: Leap year!)

2. Exception: Century years are NOT leap years UNLESS they can be evenly divided by 400.
(For example, 1700, 1800, and 1900 were not leap years, but 1600 and 2000, which are divisible by 400, were.)

(Factmonster)

Leap year is meant to correct the calendar:

again from Factmonster:
A Quick History Lesson

The Egyptians were the first to come up with the idea of adding a leap day once every four years to keep the calendar in sync with the solar year. Later, the Romans adopted this solution for their calendar, and they became the first to designate February 29 as the leap day.

But Wait! It's Not Quite that Simple!

The math seems to work out beautifully when you add an extra day to the calendar every four years to compensate for the extra quarter of a day in the solar year. As we said earlier, however, the solar year is just about 365 ¼ days long—but not exactly! The exact length of a solar year is actually 11 minutes and 14 seconds less than 365 ¼ days. That means that even if you add a leap day every four years, the calendar would still overshoot the solar year by a little bit—11 minutes and 14 seconds per year. These minutes and seconds really start to add up: after 128 years, the calendar would gain an entire extra day. So, the leap year rule, "add a leap year every four years" was a good rule, but not good enough!

Calendar Correction, Part II

To rectify the situation, the creators of our calendar (the Gregorian calendar, introduced in 1582) decided to omit leap years three times every four hundred years. This would shorten the calendar every so often and rid it of the annual excess of 11 minutes and 14 seconds. So in addition to the rule that a leap year occurs every four years, a new rule was added: a century year is not a leap year unless it is evenly divisible by 400. This rule manages to eliminate three leap years every few hundred years.

Answer 3

The Gregorian calendar, the current standard calendar in most of the world, adds a 29th day to February in all years evenly divisible by 4, except for centennial years (those ending in -00), which receive the extra day only if they are evenly divisible by 400. Thus 1600, 2000 and 2400 are leap years but 1700, 1800, 1900 and 2100 are not.