Provided are ultraviolet (UV)-curable polyols and polyurethane compositions made by reacting the inventive polyol with an isocyanate. The inventive ultraviolet (UV)-curable polyol is made by co-polymerizing an alkylene oxide, an unsaturated carboxylic acid or anhydride and a hydroxy functional compound in the presence of a double metal cyanide (DMC) complex catalyst such that the polyol has an ultra-low level of unsaturation. The inventive polyols may be used to produce prepolymers, which in turn may be useful in making thin films which in turn may provide such items as medical examination gloves and scientific gloves. The inventive ultraviolet (UV)-curable polyurethane compositions may also find use in or as coatings, adhesives, sealants, elastomers and the like.