Question

Given the algorithm in the leap year case study

Divide the year by 4 and if the remainder isn't 0Return false (The year is not a leap year)Otherwise, divide the year by 100 and if the remainder isn't 0,Return true (The year is a leap year)Otherwise, divide the year by 400 and if the remainder isn't 0,Return false (The year is not a leap year)Otherwise, Return true (the year is a leap year)
Decide whether the following years are leap years:
a. 1900
b. 2000
c. 1996
d. 1998

Answer 1

The years 1900 and 1998 are not leap years, while the years 2000 and 1996 are. This determination follows the Gregorian calendar rules that account for the average length of the year to approximate the tropical year.

Step-by-step explanation:

According to the Gregorian calendar, which is the system currently used to identify leap years, we follow a specific set of rules to determine whether a year is leap or not. Let's apply those rules to decide whether the following years are leap years:

• 1900: Divide by 4, the remainder is 0. Divide by 100, the remainder is 0. But, dividing by 400 gives a remainder, so 1900 is not a leap year.
• 2000: Divisible by 4, 100, and 400. Therefore, 2000 is a leap year.
• 1996: Divisible by 4 and not a century year, so it doesn't need to be checked by 400. Hence, 1996 is a leap year.
• 1998: Not divisible by 4, so 1998 is not a leap year.

The Gregorian calendar refined the system used by the Julian calendar to better align with the solar year, adding complexity to the leap year determination by including the divisible-by-400 rule for century years, to correct the average calendar year length closer to the tropical year.