A sensor unit and an associated transmitter unit are enclosed, or encased, within a housing, to form a monitoring device, and a thus formed monitoring device is positioned either inside or outside of each tire to be monitored. For tires that are 18 inches or smaller, the monitoring device is preferably attached to the bottom of a specially designed valve stem that is secured to the vehicle's tire where the monitor is located within the tire. For tires that are 20 inches or larger, the monitoring device is preferably attached to the side of another specially designed valve stem that is secured to the vehicle's tire where the monitor is located outside the tire. The same monitoring device is used for each location.