What is the date of the 100th day in the calendar year?

To determine the 100th day of the year, we need to account for whether it is a leap year or a common year.

In a Common Year (365 days):

A common year has 365 days, and the days are distributed as follows:

• January has 31 days.
• February has 28 days.
• March has 31 days.
• April has 30 days.
• May has 31 days.
• June has 30 days.

Let’s calculate the 100th day step-by-step:

1. January: 31 days.
2. February: 28 days.
   • So far, 31 (January) + 28 (February) = 59 days.
3. March: 31 days.
   • After March, 59 (January + February) + 31 (March) = 90 days.
4. April: 30 days.
   • The 100th day falls in April, because 90 (up to the end of March) + 10 = 100.

Thus, the 100th day of a common year is April 10th.

In a Leap Year (366 days):

A leap year has 366 days, and the days are distributed as follows:

• January has 31 days.
• February has 29 days.
• March has 31 days.
• April has 30 days.
• May has 31 days.
• June has 30 days.

Let’s calculate again, considering the extra day in February (29 days):

1. January: 31 days.
2. February: 29 days.
   • So far, 31 (January) + 29 (February) = 60 days.
3. March: 31 days.
   • After March, 60 (January + February) + 31 (March) = 91 days.
4. April: 30 days.
   • The 100th day falls in April, because 91 (up to the end of March) + 9 = 100.

Thus, the 100th day of a leap year is April 9th.

Summary:

• In a common year, the 100th day is April 10th.
• In a leap year, the 100th day is April 9th.