Why is my MOSFET switch not behaving as expected?

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I have the following circuit wired up on a protoboard.

PZlmB.png


The datasheet for the BSS138 MOSFET is here. I'm puzzled regarding what I'm seeing happen with this circuit - when I apply 3.3V at the gate resistor, the MOSFET turns on fully and I see 3mV at the output. This, of course, is expected.

However, if I remove 3.3V from the gate resistor, the pull-down resistor turns the gate off. I expected to see approximately 3.3V at the output, yet I only see 2.7V. If I replace the 3.3V on R1 with 5V, the output shows 4V. In other words, a volt is being dropped on R1 when the MOSFET is off. Is this expected? Somehow, I expected the MOSFET to have an immensely high resistance when off and hence expected approximately 5V being dropped on it when it's off.

Are my expectations wrong for this MOSFET?
 
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What is the Output tied to . . some kind of load?
 
One way this could happen is if you used an analog voltmeter to do the measurements.

If it drew about 1 mA while taking the measurements, you would get voltage readings like this..

It could also just be a faulty FET.

One easy test would be to put a milliammeter in series with the supply and see if you can cut off the current when the gate voltage is dropped to zero.