A fraction of a unit is still the same unit.

$0.05 dollars is still dollars... That would be why it's stil notated with $... The same way we still notate sats as 0.007 Bitcoin. But we use cents to describe a fractions of dollars. Cents are not different assets from dollars. They are fractions of one. Sats are fractions of Bitcoins. You can note cents with ¢. Same way you would notate a fraction of a Bitcoin with the sats symbol. $ =/= ¢ but they are the same asset