1.6 Significant Figures - University Physics Volume 1 _ OpenStax.pdf

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5/21/20201.6 Significant Figures - University Physics Volume 1 | OpenStax1/8Learning ObjectivesBy the end of this section, you will be able to:Determine the correct number of significant figures for the result of a computation.Describe the relationship between the concepts of accuracy, precision, uncertainty, and discrepancy.Calculate the percent uncertainty of a measurement, given its value and its uncertainty.Determine the uncertainty of the result of a computation involving quantities with given uncertainties.Figure 1.11shows two instruments used to measure the mass of an object. The digital scale has mostly replaced the double-pan balance inphysics labs because it gives more accurate and precise measurements. But what exactly do we mean byaccurateandprecise? Aren’t they thesame thing? In this section we examine in detail the process of making and reporting a measurement.Figure 1.11(a) A double-pan mechanical balance is used to compare different masses. Usually an object with unknown mass is placed in one pan and objects of knownmass are placed in the other pan. When the bar that connects the two pans is horizontal, then the masses in both pans are equal. The “known masses” are typically metalcylinders of standard mass such as 1 g, 10 g, and 100 g. (b) Many mechanical balances, such as double-pan balances, have been replaced by digital scales, which cantypically measure the mass of an object more precisely. A mechanical balance may read only the mass of an object to the nearest tenth of a gram, but many digital scalescan measure the mass of an object up to the nearest thousandth of a gram. (credit a: modification of work by Serge Melki; credit b: modification of work by Karel Jakubec)Accuracy and Precision of a Measurement
5/21/20201.6 Significant Figures - University Physics Volume 1 | OpenStax2/8Science is based on observation and experiment—that is, on measurements.Accuracyis how close a measurement is to the accepted referencevalue for that measurement. For example, let’s say we want to measure the length of standard printer paper. The packaging in which wepurchased the paper states that it is 11.0 in. long. We then measure the length of the paper three times and obtain the following measurements:11.1 in., 11.2 in., and 10.9 in. These measurements are quite accurate because they are very close to the reference value of 11.0 in. In contrast, ifwe had obtained a measurement of 12 in., our measurement would not be very accurate. Notice that the concept of accuracy requires that anaccepted reference value be given.Theprecisionof measurements refers to how close the agreement is between repeated independent measurements (which are repeated underthe same conditions). Consider the example of the paper measurements. The precision of the measurements refers to the spread of the measured

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