A day is a day. When I was freelance I just billed a day rate. The point for me is that I simply don't count the hours. It just meant I would spend the day working on that clients project only. Typically I'd do something like around 9-17:30, with around an hour for lunch. So that works at 7h30. But sometimes I stopped earlier. Sometimes I worked later. I still billed the same.
I never pro-rated the invoices for partial days. My minimum billing increment was half a day on the odd occasion I needed to run an errand that was going to require less than a full day off.
