Example 1-2. According to the relaxed definition, the error in our measurement of me is
(9.15 - 9.11) × 10⁻³¹ kg = 0.04 × 10⁻³¹ kg.
Notice that the accepted value of me was rounded up to 9.11 × 10⁻³¹ kg because it would be pointless to use more significant figures in the accepted value than there are in the measured value.
There is a belief that quantities such as the mass of an electron have a true value and perfecting the measurement process would give better and better approximations to this true value. In contrast, there are many examples in which a true value is unknown because the value is not well defined. For example, the thickness of a block is unknown since even a very highly polished block has rough surfaces when viewed at high magnification. Therefore, the distance from one side is not well defined and improving the measuring instruments beyond some point would do no good.
2. Relative error is the error in a quantity divided by the quantity.
3. Uncertainty means the estimated reliability of a value. There are various ways to make this estimate and the main purpose of this first "experiment" is to gain skill in evaluating and expressing uncertainty. Thus, the figure 0.0000054 × 10⁻³¹ kg in the above-quoted mass of the electron is the uncertainty.
4. Relative uncertainty is the uncertainty in a value divided by the value. It may be expressed as a fractional decimal or as a percentage.
Exercise 1-1. Find the relative uncertainty in the mass of the electron.
5. Discrepancy means the difference between two measured values of a quantity. We shall measure the value of the acceleration due to gravity, g, several times during the semester. Suppose that we get g = 9.910 m/s² and 9.805 m/s² using two techniques. The discrepancy in the two values is 0.105 m/s². In the Appendix on p. 101, we find the accepted value of g = 9.797 m/s² for Northridge.
Exercise 1-2. What are the errors in the measured values g = 9.910 m/s² and 9.805 m/s²? The relative errors?