Now I feel like a moron.
I did turn it upside down but I couldn't see the battery compartment.
I've had the scale for at least five years and haven't ever changed the battery!!
(as it happens, nobody was at the gym tonight and so I got nekkid and stepped on the scale, which showed 264. Then at home I got 265, 266 and 267, so I'm not claiming mini-goal, yet...)