2.1. Errors when Reading Scales

The most common measurements in the lab are done with devices that have a marked scale. Let's look at an example. In one of your first experiments you will measure the length of a pendulum from the pivot point to the center of the mass attached to its end point. Let's first simplify the situation a little bit. We will measure the length of the pendulum from the pivot point to the visible end of the mass. The situation is schematically shown in the figure below

(numbers are in centimeters)

Even using this idealized, zoomed-in picture, we cannot tell for sure whether the length to the end of the mass is 128.89 cm or 128.88 cm. However, it is certainly closer to 128.9 cm than to 128.8 cm or 129.0 cm. Thus we can state with absolute confidence that the length L is

We call the first term, 128.9 cm, the "central value" and the second term, 0.1 cm, the "error" or "uncertainty".

If pressed, we could get a little bit better precision from the picture. However, in a real situation, the precision of 0.1 cm for measurements done with the centimeter ruler is as good as you can get.