You are standing on a scale in an elevator when the cable snaps, sending the elevator car into free fall. before the automatic brakes stop your fall, you glance at the scale reading. does the scale show your real weight? an apparent weight? something else?

It will show an apparent weight of zero.

Explanation:

The scale reads the force that the object on it exerts which is equal to the normal force exerts in the object by the scale. When the acceleration is equal to zero, the force read by the scale is in magnitude equal to the true weight  (this true weight is always going to be your mass times the acceleration due to the force of gravity).

When the elevator is falling in free fall, means only the force of gravity is acting over the objects falling, so there is no normal force exerted form the scale to your feet, and if this normal force is equal in magnitude to the force read by the scale, the scale s going to show a 'zero' for the weight.