[naniwaduni]

Picking 1/10^9 would also have had the advantage of making the distance from the pole to the equator ~1 gigacentimeter.

Exploring a bit, picking 4 times that, as an estimate of the circumference, would give us a basic length unit of 4 cm (a pretty reasonable unit—bit over an inch and a half, fits right in with the variety of Chinese cun standards, for example). Then our immediate volume unit is 64 mL, which seems kind of small (on the scale of 2 floces), but ten of them make a decent "pint", so I think it can work—it's ~13% bigger than an imperial pint instead of ~12% smaller. the corresponding mass unit, at ~64 g, which again seems a bit small but manages to line up an average person's weight right around 1 kilo.