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The mathematics of error analysis, though reviewed in measurements books and laboratory manuals, is rarely experimentally applied at an elementary level. An approach based on experiments that investigate and specifically illustrate measurement errors on a basic level is described. The purpose in introducing these experiments on an elementary level is to develop in the student both an ability to understand and analyze experiments and data with respect to errors, and an understanding of the interrelationship between the theory and the experimental implementation of a measurement. Furthermore, there is a need for the student to be able to design measuring systems and develop techniques with minimal complexity to satisfy specific accuracy and tolerance requirements. This approach is implemented by a sequence of experiments, two of which are described in detail. The first of these experiments, "Measurement Errors," is concerned with error weights and the concepts of accuracy, precision, resolution, and consistency of measurements and measuring systems. In the second experiment described, the principles of digital and analog measurements and their associated errors are investigated.