Question

How many years have 29 days in February from 2001 to 2100.

Answer 1

Answer:

24

Step-by-step explanation:

2004 is the first year after 2001 to be a leap year

2096 is the last year before 2100 to be a leap year

A leap year happens every 4 years

a1 = 2004

an = 2096

d = 4

Solve n:

an = a1 + (n - 1)d

2096 = 2004 + (n - 1)4

2096 = 2004 + 4n - 4

2096 = 2000 + 4n

4n = 96

n = 24

Answer: There are 24 years with that February has 29 days from 2001 to 2100.

Answer 2

Answer : $\bold{24 \: years}$



Explanation -

Two Rules -

Ending with two 0's are century years like 2000, 2100. etc

Not ending with two 0's are Non Century years like 2001, 2002 etc.


Century Year -

It is a leap year, if the century year is divisible by 400.

2000 ÷ 400 = 5. So, year 2000 is a leap year .

2100 ÷ 400 = 5.25. So, year 2100 is not a leap year.



Non Century Year -

It is a leap year, if the Non Century year is divisible by 4.

2004 ÷ 4 = 501. So, year 2004 is a leap year .

So, For 100 years there are supposed to be 25 leap years when the year is divisible by 4 like - 2004, 2008, 2012 ......... 2092, 2096, 2100.


But 100 is a century year which is not divisible by 400. So, 2100 is not a leap year .

So, exclude the century year 2100 which is not leap year.

25 - 1 = 24.

There are 24 leap years from 2001 to 2100.


Hence :

It is a leap year when the Non Century year is divisible by 4 and Century year is divisible by 400.