The voltage drops measured across very high value resistors do not add up - why is that?
Your meter is affecting the measurement

Your voltmeter is also connected to the circuit, and in a different position for each of your two measurements.  A "perfect" voltmeter would have an infinite resistance, but any real voltmeter has a non-infinite one.  So some current flows through it, and that affects your measurement. So your actual measurements look like this:







simulate this circuit &ndash; Schematic created using CircuitLab

The first one is fine, the meter still measures the battery voltage. In the second one, the meter is in parallel with R1.  This reduces the effective resistance of the top half of the potential divider, and reduces the voltage across it.  In the third case, the resistor meter is in parallel with the bottom half, and reduces it.  So the total comes to less than 3.68V.

Bonus: You have enough information here to calculate the resistance of the meter.  Can you work out what it is?