My analog sensor outputs .5 to 4.5VDC. How do you convert to analog 0-10VDC?
1-9V is easiest because it does not require offsetting (and thus no reference required). Only a couple of matched resistors to get a gain of +2.

Eg. 







simulate this circuit &ndash; Schematic created using CircuitLab

For more precision, use a better op-amp and more accurate/stable resistors. A 1% change in either resistor results in a 0.5% change in the output voltage. 

There should also be a bypass capacitor (eg. 10nF) across the op-amp power, and you may wish to place a high-value resistor to ground on the non-inverting input to make the output go below 1V if the sensor is disconnected. As drawn it will tend to go towards the positive rail because bias current flows out of this particular op-amp.