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significant figures

# significant figures - More sophisticated ways exist to...

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More sophisticated ways exist to handle uncertainties in quantities than significant figures. [For an extensive discussion, see the NIST website on Uncertainty of Measurement Results .] However, using this relatively simple formalism should create a sensitivity and appreciation for the connections between measuring devices, their capabilities, and their limitations. Many exercises involve the determination and reporting of some quantitative property. Both the value of the property and its uncertainty will be important. It is essential that each measurement that leads to the value has been made with the full capability of the devices and apparatus used in its determination. SUPL-001 contains a brief section on the concept of significant figures . As noted in that supplement: close attention will be paid to the use of significant figures in laboratory reports grading standards for exercises and quizzes invariably include a substantial number of points that deal with the proper implementation of this concept. you are urged to master this concept early in the laboratory course. We encourage the use of electronic calculators for facilitating the computations associated with experimental numbers, but, even inexpensive calculators are designed to deal with, and display, numbers having 10 or more digits. This places the burden of accounting for the appropriate representation of numerical data on the student investigator. everyday laboratory measurements limit the number of digits that represent reality the concept of significant figures seeks to limit the number of digits in a quantity to those that are justified based on its origin Two features play a role in the determination of significant figures - measurement , and computation using measured values. Measurement: for a quantity that is the result of a direct measurement, the number of decimal digits (the number of digits in the representation of the number, both to the right and the left of the decimal point) in that quantity is generally fixed by the measuring device. The number of significant digits can depend on the value of the measurement. Our rule of thumb is that, for a device whose output is linear , the eye can estimate values lying between two marks on a scale to one-fifth of the distance between the two marks. For experimentally determined quantities, the number of significant figures is not simply related to the intrinsic precision of a device. Consider the buret and the analytical balance.

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