I had a plastic ruler at one time in my life and it looked something like Figure 1.
Figure 1. Overview.
Figure 2. Close up of precision grid.
Figure 3. In-use.
How to use:
Align the right edge to the nearest whole cm less than the width of the item to be measured.
In the precision section, find the closest intersection between a sloping line and a ...
Metric bolts use thread pitch in millimeters. Your M3 screw likely uses the standard pitch of 0.5 millimeters. One complete rotation of the screw will advance the screw into the work piece by that amount.
According to the Bolt Depot chart, there is only one standard pitch for M3 screws, although other sizes will have standard, fine, super fine pitches ...
A metric thread table is what you want.
Table 1. Source: Anzor.
So is there a standard rule of thumb, or equation about the distance the end of a screw will travel per rotation?
It's not a rule of thumb - it's defined by the pitch.
Conversely, how many turns it will take to travel a specific distance?
Turns required = distance / pitch.
Say I have ...
I would give a shot at image processing, if there is a good contrast between the surface you want to measure and the background.
To do so you need to take a picture of the surface that includes an object of known size for calibration.
Then, open source software like "imageJ" are able to perform the measurement.
The accuracy of this method strongly depend on ...