They clearly treated it as a base sixty floating point system, even though they wrote each “sexagesimal digit” using collections of two symbols one of which rep

They clearly treated it as a base sixty floating point system, even though they wrote each “sexagesimal digit” using collections of two symbols one of which represented 10 times the other. The symbol for 10 was only ever used to represent 10*60^n. Tens were never themselves the unit. (Though the abstract sexagesimal system evolved out of earlier concrete systems with less standardized mixtures of physical units.)