What happens in American customary units if you need to split it into 7ths?

Significant Figures. Things are rarely one third down past 3-4 sigfigs. Maybe 6+ if you're being really precise or EDMing a part.

Good point. Splitting things in to 3rds is the most common function of everything. Why, just the other day I was building a box. I started by measuring the largest face of the backplate and subtracting the thickness of the side plates so I could figure out the internal volume. Most people would have done a simple equation like x-y but I prefer to do 3((x/3) - (y/3)). It's a much cleaner method.