Your beloved Canon PowerShot S1iS features a 10x optical zoom.
Yes, and no.
The zoom ranges from 5.8mm (at the wide angle end) to 58mm at the telephoto end. In terms of 35mm film cameras, the equivalent would be a zoom lens that goes from 38mm to 380mm. 380/38=10, goes the math.
The problem is that 38mm is not the normal view; it is the wide-angle view -- wider than a "normal" photo. What's Normal? Old timers who use film-based camers know the answer: 50mm.
Strictly speaking, the zoom portion is 50mm to 380mm, which means the zoom ratio is 7.6x (380/50 - 7.6). That means that objects at maximum zoom appear 7.6x larger than normal. That's as powerful as many binoculars.
Adding in the 3.2x digital zoom, the total true zoom amounts to 24.3x (7.6x multiplied by 3.2x).