# Errors, Uncertainties, and Measurements

Topics: Measurement, Measuring instrument, Metrology Pages: 10 (3074 words) Published: June 30, 2013
Experiment 1: Errors, Uncertainties, and Measurements
Laboratory Report

Margarita Andrea S. de Guzman, Celine Mae H. Duran,
Celina Angeline P. Garcia, Anna Patricia V. Gerong

Department of Math and Physics
College of Science, University of Santo Tomas
España, Manila

Abstract

Measurements, defined as a comparison with a standard, are essential in the study of physics. However, all measurements are prone to errors. There are two sources of errors: systematic errors random errors. This experiment aims to show how errors are encountered in measuring an object. Three instruments, namely the foot rule, vernier caliper, and micrometer caliper, were used to measure the diameter of a metal sphere. Ten independent measurements were taken per instrument. Statistical computations were performed to show the accuracy and precision of each instrument. Upon computation of the volume and density of the sphere based from the mean diameter, the percent error for each instrument was computed. At the end of the experiment, it was found that the micrometer caliper is the most accurate instrument in finding the diameter, while the foot rule is the least accurate.

I. Introduction

As early as the ancient times, the need for simple measurements presented itself in tasks, such as constructing houses, sowing clothes, knowing how heavy objects are, and telling time. The early units of measurements, as evidenced by writings by Babylonians and even the Bible, were based from the body parts of humans. Thus, the ancient terms digit, palm, span, and cubic were all derived from human body parts, which later on evolved into the English system of inch, foot, and yard. Time was measured by periods of sun, moon, and other heavenly bodies. Much later on, during the 16th century, the need for a standard unit of measurement worldwide was recognized. During the French revolution in 1790, the National Assembly of France delegated to the French Academy of Sciences the task of deducing “an invariable standard for all the measures and all the weights.” From then on, a simple and scientific system called the metric system was invented. Today, units derived from the metric system are known as the International System of Units.

To measure is to compare the magnitude of an unknown quantity with some standard quantity of the same rates. In this experiment, instruments were used in measuring the diameter of a metal sphere. The first instrument is a foot rule, which is one foot (12 inches) in length. It has units in inches, as well as centimeter on the opposite side. Another is called a vernier caliper which is a slide-type caliper that can be used to measure internal and external distances and depths accurately, with a reading error equal to 1/20 mm = 0.05 mm. Lastly, a device called the micrometer caliper was used to measure very small distances beyond the hundredths of a centimeter measuring to 10-6m, or 1 micrometer.

All measurements have uncertainties associated with them, no matter how advanced the measuring instrument is. The deviation of a measurement from the correct or true value is called as the error. It is a measure of the inaccuracy of the results. In general, there are two types of error based on how these errors are achieved. Systematic errors are associated with a particular measuring instrument or experimental technique. These types of errors can be reduced by proper calibration of instruments, or by following proper techniques in measuring and use of instruments to reduce human errors. On the other hand, there are errors that are brought about by uncontrollable factors, or errors that occur statistically such as when the data deviates from the true value. These errors are called random errors, and can be reduced by repeating measurements.

Associated with error are the terms accuracy and precision. Accuracy refers to how near a measured value is to the true value. Precision, on the other hand, is a measure of how close...

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