Help understanding how op amps work
Now that the op amp is introduced, my understanding starts to break down. This op-amp says it has a gain of 10, does this mean that 10V or 50mV should be the measured drop across the oscilloscope? 


What's \$V_{in}\$? 

Whatever \$V_{in}\$ is, the voltage of the output source is 10x that.

Then, the voltage seen by the oscilloscope is determined by that value, and the resistor divider formed by the op-amp's output resistance and the oscilloscope's input resistance.

(Hint: Neither of your proposed answers is correct)