Some issues with voltage drops ???

Suppose that you connect only one end of a resistor to the positive
terminal of a 9V (9.23 actual) battery and use a DVOM to measure the
voltage drop between the other end of the resistor and the negative
terminal of the battery. Is the voltage drop across these two points
always going to be 9.23V regardless of the size of the resistor?
Using a 1K and 2K resistor my DVOM measured 9.23, but measured 8.39
with a 1M resistor.

I also did some experimenting with a silicon diode and a 741 op amp.
I am using two 9V batteries to make a +/- 9V power supply. I have a
voltage divider supplying 4.07 (couldn't adjust to exactly 4.0) volts
to the non-inverting terminal and a silicon diode connected between
Vout and the inverting terminal (cathode on the non-inverting side).
On paper, I was expecting to have about 4.67V at Vout and a few micro
volts below 4.07V at the inverting terminal. What I ended up getting
in the real world was 4.26 at Vout and 4.07 at the inverting
terminal. The diode is dropping about 0.2 volts instead of the
typical 0.6 ???

Doing some more experimenting I made up a different circuit using just
a singe 9V battery, voltage divider (POT), and the same diode.
Connecting the anode side of the diode to the output of the voltage
divider and measuring the voltage drop between the free end of the
diode and the negative terminal of the battery produced values ranging
between .20 and .29 volts. Why am I not getting voltage drops around .
6V?

If I make a complete circuit putting the diode in a series with a
resistor, I can get a voltage drop of 0.6 across the diode so I thing
that the diode is working ok.

Any help would be greatly appreciated. Thanks
.

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