A comparison is made of the sensitivities for detecting hydrogen with Pt-coated single ZnO nanorods and thin films of various thicknesses (20-350 nm). The Pt-coated single nanorods show a current response of approximately a factor of 3 larger at room temperature upon exposure to 500ppmH2 in N2 than the thin films of ZnO. The power consumption with both types of sensors can be very small (in the nW range) when using discontinuous coatings of Pt. Once the Pt coating becomes continuous, the current required to operate the sensors increases to the μW range. The optimum ZnO thin film thickness under our conditions was between 40-170 nm, with the hydrogen sensitivity falling off outside this range. The nanorod sensors show a slower recovery in air after hydrogen exposure than the thin films, but exhibit a faster response to hydrogen, consistent with the notion that the former adsorb relatively more hydrogen on their surface. Both ZnO thin and nanorods cannot detect oxygen.