Koz writes:

Just curious about something here. Along the same line as the "which
side of the car should the gas filler be on", 1:51.2 seems like a weird
and arbitrary gearing. I can assume that it was just conventiently
fitting gears that matched some existing enclosure casting or something
like that but is there some logical reason someone would need 1:51.2 vs
1:50, 1:60 or something more "round"?

The explanation I've heard is that if the gear ratio is an exact
integer, the same teeth will engage each other for every revolution of
the gear. If one tooth has a flaw, it will quickly grind a matching flaw
into the corresponding tooth on the other gear, causing various bad
things to happen.

If the gear ratio is not an exact integer, the wear gets distributed
among all the teeth, and the gear lasts longer (at least in theory).