If you have a 10 meg ohm input on a DVM, you can read 16 volts on the meter if you put a 160 megohm resistor in series with your 250 volts.

You still have current (in amps)running through that series ckt. though. Roughly 1.5 micro amps I think...

This is a tough one, because current flows if you make a complete circuit with your resistor... no matter what. That never changes.

I agree that you probably should not be using 250 volts for this experiment, until you figure this out. Try 25 volts, much safer.

Looking at this made me remember that, even though meters read out in VOLTs, it's really the CURRENT flowing through them (very, very tiny current) that gives the voltage indication.

An "ideal" meter could still indicate volts with zero current flowing, hasn't happened yet...

and a meter measuring current, is usually, actually measuring voltage across a known resistance.

Oh, and maybe the most important thing to remember, the TOPIC was "voltage resistance" well, that is not what a resistor does. it can "drop" the voltage at a point in a series circuit, but it can only "resist" if there is CURRENT flowing. So really, it's voltage dropping... and CURRENT resistance.