I just ran a completely new 10 gauge wire for my newly relocated clothes dryer. I wired up the breaker and turned if off, and turned the main breaker back on. When I measure voltage between the black and white OR between the red and white even though the breaker is OFF I get 1.3 volts. How concerned should I be and how do I troubleshoot the problem?

There is no problem to troubleshoot, you are seeing a stray induced voltage being measured by the meter, perhaps due to the calibration of the meter itself. Is this meter a $25.00 unit?

I have a Fluke meter that costs over $100, and it picks up small voltages when I touch wires that aren't energized. I stopped paying attention to it.

Is this meter a $25.00 unit?

Not a cheapie, but not a top of the line, either. I feel better now that I've seen the responses here. Thanks!