[Maths Class Notes] on Leap Year Pdf for Exam

It takes approximately 365.25 days for our planet Earth to orbit the Sun — that is a solar year. We usually round the days in a calendar year to 365, that is 365 days in a year. To make up for the missing partial day, we add one day to our calendar approximately every four years and that is known as a leap year.

In an ordinary year, if you were to count all the days in a calendar from January to December, you’d count it as 365 days. But approximately every four years,  the month of February has 29 days instead of 28. So, there are 366 days in the year. This is called a leap year.

 

Why Do We Have Leap Years?

A year can be defined as the amount of time it takes any planet to orbit its star one time. A day can be defined as the amount of time it takes a planet to finish one rotation on its axis.

It takes our planet Earth approximately 365 days and 6 hours to orbit the Sun, that is, it takes Earth approximately 24 hours — 1 day — to rotate on its axis. So, our one year is not an exact number of days.

Because of that, we round the days in a year down to 365 for most years. However, that one day doesn’t disappear. To make sure that we count that extra part of a day, we add one day to the calendar every four years. Here’s a table that shows how it works:

 

 

Because we’ve subtracted approximately six hours — or we can say that ¼ of a day — from 2017, 2018, and the year 2019, we have to make up that time in 2020 and that’s why we have a leap day!

 

Evaluation of Leap Year

The leap year occurs every 4 years, but there are scenarios where the gap between two leap years was 8 years instead of the regular 4 years.

Example: The year 1896 is a leap year. The next leap year comes in 1904 (The year 1900 is not a leap year).

In order to make the investigation easier, any year which is divisible by the number 4 completely (that is the remainder becomes zero) is considered as a leap year.

Example: 1888, 2012, 2016 are known to be leap years as it’s completely divisible by 4. Years like 2009, 2019, etc. are not divisible by 4 completely, therefore, they are normal years.

 

An Exception to Note:

A year 700 is completely divisible by 4, but this year is not considered as a leap year. For a century, the logic follows that any year should always be divisible by 400 not by 4. Even though the year 700 is divisible by 4 but not by the number 400. Hence, we cannot consider the year 700 as a leap year.

Example: 400, 800, 1200, etc. are leap years as they are divisible by 400, and years 300, 700, 100, etc are not leap years as these years are not divisible by 400.

 

Why?

We have discussed above, we know that because the Earth rotates about 365.242375 times a year but a normal year is 365 days, something has to be done to “catch up” the extra 0.242375 days a year. 

• So every fourth year we add an extra day (the 29th of February), which makes 365.25 days a year. This is fairly close but is wrong by about 1 day every 100 years.

• So every 100 years we don’t have a leap year, and that gets us 365.24 days per year (1 day less in 100 years = -0.01 days per year). Closer, but still not accurate enough!

• So another rule says that every 400 years is a leap year again, this gets us 365.2425 days per year (that is 1 day regained every 400 years equals 0.0025 days per year), which is close to 365.242375 not to matter much.

How to Determine Whether Any Year is a Leap Year?

To determine whether any given year is a leap year, follow these steps:

1. If the year is evenly divisible by four, then go to step 2. Otherwise, go to step 5.

2. If the year is evenly divisible by a hundred, then go to step 3. Otherwise, go to step 4.

3. If the year is evenly divisible by four hundred, then go to step 4. Otherwise, you can go to step 5.

4. The year is a leap year (if it has 366 days).

5. The year is not a leap year (if it has 365 days).