Keeping Time with the Skies - Solar calendars

Determine if the year $1900$ was a leap year according to the Gregorian calendar rules.

$1900 \div 4 = 475$ (Divisible by $4$) $1900 \div 100 = 19$ (It is a century year) $1900 \div 400 = 4.75$ (Not divisible by $400$)

Since $1900$ is a century year, it must be divisible by $400$ to be a leap year. Because $1900$ is not divisible by $400$, it was not a leap year.

Calculate the difference (error) between a calendar year of exactly $365.25$ days and the actual solar year of $365.2422$ days.

To find the difference, we perform subtraction: $\begin{array}{r} 365.2500 \\ -365.2422 \\ \hline 0.0078 \end{array}$

The calendar year of $365.25$ days (used in the Julian calendar) is longer than the actual solar year by $0.0078$ days. Over $1000$ years, this error accumulates to $7.8$ days.

How many days are there in $4$ consecutive years if one of them is a leap year?

$\text{Total days} = (3 \times 365) + 366$ $\text{Total days} = 1095 + 366 = 1461$

Three non-leap years have $365$ days each, and the leap year has $366$ days. The sum gives the total number of days in a $4$-year cycle.