Adjustable pots, potentialmeter?

I need to finish my current project and I need to find or build an adjustable unit which capable to adjust from about 829 ohms to about 2.66k and I was thinking of using a 680 ohms resistor inline with a 2 k potentialmeter (adjstable pot) so that way I wouldn't go beyond the 2.66k max but still okay on the low side at 680ohms.However, after spoken to a friend of mind and he told me a 2k pot doesn't neccessary measure 0 ohm at its lowest setting.Can someone confirm that?If that's the case is there any other alternative to get around this?Thank you guys for your help!

Obviously everything that we build will have some type of resistance. I really don't know what the actual resistance of the 2k pot is but it cannot be 0. Good luck in finding your answer.If your counting pennies and dimes then maybe you shouldn't be spending every penny and dime you have!!