Is it a fact or fiction that the earth rotates about its axis approximately 366.25 times for each revolution about the sun?

It's a fiction.

The extra revolution is the “big” circle around the sun. Hold a dime fixed on the table. Put another dime against it and roll it around. The one you roll gets 2 revolutions.

This is fiction. It's 365.25 days a year.

This is fiction. It's 365.25 days a year.

Fact

Hard to believe, we know. To simplify it, a day is defined by the time it takes for the sun to get to the same part of the sky as it was the day before. It takes more than one spin to complete a day, because we have to make up for the distance weve moved around the sun. If youre still confused, see the source below. source: https://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970714.html (subheading: the suns path in the sky)