SOLUTION: It takes Earth approximately 365.2422 days to orbit the sun once, this is known as the tropical year and is the length of the cycle of seasons. In a regular year, there are 365 day

Question 1023225: It takes Earth approximately 365.2422 days to orbit the sun once, this is known as the tropical year and is the length of the cycle of seasons. In a regular year, there are 365 days, and in a leap year there are 366 days. In a four-year period, one year being a leap year, what is the absolute difference between the number of days observed in the calendar years and the number of days in four tropical years? Express your answer as a decimal to the nearest ten-thousandth.
Thank you and please show all work to get you to the solution. Thanks
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The number of days in a period of four consecutive calendar years where one year is a leap year is the integer number
,
which we can express as to the nearest ten-thousandth,
because is one ten-thousandth.
The number of days in four orbits of Earth is the non-integer number
.

The difference is
.

NOTES:
1) The length of the tropical year changes a little over the centuries, but for now is a good approximation.
(I did not know that before your question, so thank you for the learning opportunity).
Since is a good approximation,
we do not have to worry about , given with 4 decimal places,
not being precise enough to make not being to the nearest .

2) Calendar years are leap years if divisible by , but not by unless divisible by ,
so in years there are leap years,
and the average length of a calendar year is .
(I was taught that in the 9th grade, and it stuck with me).
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