What is the exact number of days in one year?

The  number of days in a year is 365 days.

Once in 4 years normally we observe a leap year.

But every 4th year is  not leap. The century years are exceptional. Only the century years divisible by 400 is leap. Not other century  years which are not divisible by 400.

So by this we can calculate that in 400 years there are 400*365days +400/4 days - 3days for 3 non leap century years = (146000+100-3)days = 146097 days.

So in one year there are 146097/400 days = 365.2425 on an average.

An year is the period earth takes to go round the sun and come back to to the exact /same position on the ecliptic. Normally in astrnomy we say this fixed point as 1st point of Aries. The first point of Aries also recedes by a very small measure called precission. So in astronomy this period of rotation is called a tropical year  whose value is  365 days, 5 hours, 49 minutes, and 12 seconds nearly.