who determine that it should be 365/366 days in a year?

the earth completes a complete revolution every 365.25 days. The .25 gets rectified every 4 years with leap year. It take the earth 24hrs to complete 1 rotation. Or 365.25 rotations complete 1 revolution.

No-one has actually 'determined' the days and hours. It;'s just the way it is. We use years, months, weeks, days, hours, minutes and seconds purely as a measuring device for the explanation of time. We know that the earth revolves around the sun once every 365 1/4 days (hence the need for a Leap Day in every 4 years). We know that during that period the earth revolves the same number of times so a 'year' and a 'day' are pretty much already predetermined. Using the measurement of 'miles' we know that the circumference of the earth is 24,859.82 miles. As the earth is not a perfect sphere but elliptical an average circumference is more like 24,000 miles so dividing a 'day' into 24 'hours' is logical as each hour is the time taken for the earth to revolve 1,000 miles. An hour is more interesting.

The importance of 60 comes from the Babylonians used a base 60 number system as compared to our base 10 system. 60 and 6x60 = 360 were very natural numbers for them to work with. They used a 360 (6X60) day calendar as opposed to our 365 day calendar. The ancient astronomers would have noticed that it takes 365 days for the sun to move (about our fixed Earth) past the stars that appeared to be fixed to an external heavenly sphere, and return to where they started. The choice of 360 days for a year may have been a compromise between a 365 day solar year and a 354 day lunar year, (consisting of 12 months of 29.5 days each).

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there are 365 and 1/4 days in a year. there are of course 24 hours in a rotation. It takes you one year to to do a revolution. but for a rotation it only takes u one day.

This determination was originally made by Pope Benedict in 1157 and then reaffirmed by Johan Sebastian Bach and Polpot (of Cambodia) 104 years later, on the anniversary of the mongolian rise to power. The number is derived from a complex mathematical analysis of the bible. Entire mosques of monks spent years recording approximate time passage in the bible and determined that it indicated 345 days passing per year. this was then increased to 365 as the pope added multiple religious holidays to the calendar. The extra day, during leap years, was set aside as a day for all other religions to celebrate, but made to occur once every 4 years.

you are correct on both