Remember too that there was no zero at the time.
If you watch the movie Zeitgeist, they have what appears to be a logical explanation for three days.
Think of it like a hotel stay. He couldn’t check in until the afternoon on Friday, and he had to check out on Sunday morning so housekeeping could take care of the tomb. Three days, two nights, just like the travel agent says.
Although, given that he apparently did not leave his room all day Saturday, I have to imagine that the minibar bill was outrageous.
What, with a faucet full of water?
I was just going to post this as well. It’s a way of counting days that is quite common. And considering that the phrase in the Apostle’s Creed just before the “rose again” phrase is “he descended into hell”, it has some similarities. 
Well, it gets complicated if you take the Sign of Jonah into consideration. Jesus said:
“An evil and adulterous generation seeks after a sign, and no sign will be given to it except the sign of the prophet Jonah. For as Jonah was three days and three nights in the whale’s belly, so shall the Son of man be three days and three nights in the heart of the earth” (Mt 12:40)
So…three days AND three nights?
I’ve wondered the same thing as the OP for a long time.
Καὶ ἀναστάντα τῇ τρίτῃ ἡμέρᾳ
Kai anastanta tē tritē hēmera
Nicene Creed