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Ground movements and monitoring
Published in David Chapman, Nicole Metje, Alfred Stärk, Introduction to Tunnel Construction, 2017
David Chapman, Nicole Metje, Alfred Stärk
It is important to understand the quality of the data received from instrumentation. For this reason, some important definitions related to monitoring and instrumentation are given below (after Dunnicliff and Green 1993): Conformance: the presence of the measuring instrument should not alter the value of the parameter being measured. The degree by which the parameter is altered by the instrument is known as its conformance.Accuracy: this is the closeness of a measurement to the true value of the quantity measured. Accuracy is synonymous with degree of correctness. The accuracy of an instrument is evaluated during calibration to a known standard value. It is customary to express accuracy as a ±number.Precision: this is the closeness of each of a number of similar measurements to the arithmetic mean. Precision is synonymous with reproducibility and repeatability. The number of significant figures associated with the measurement indicates precision. For example, ±1.00 indicates a higher precision than ±1.0.
Decimals
Published in John Bird, Basic Engineering Mathematics, 2017
(a) 4 decimal places, (b) 3 significant figures0.004369=0.0044 $ 0.004369 = \mathbf{0.0044} $ correct to 4 decimal places.0.004369=0.00437 $ 0.004369 = \mathbf{0.00437} $ correct to 3 significant figures.Note that the zeros to the right of the decimal point do not count as significant figures.
Error Analysis
Published in James P. Howard, Computational Methods for Numerical Analysis with R, 2017
Significant digits, also called significant figures, are the parts of a number that include the precision of that number. This is limited to any non-zero digits in the representation of the number. The significant digits convey all of the precision of a number. For instance, the number π $ \pi $ can be represented as 3, 3.1, 3.14, 3.142, 3.1416, 3.14159, and so on with an increasing number of significant digits. Accordingly, as the number of significant digits increases, so does the precision of the estimate.
Using simple algebraic concepts to understand chemical composition problems
Published in International Journal of Mathematical Education in Science and Technology, 2022
Enrico Ravera, Claudio Luchinat
As we have already seen, the sets of conditions α from the previous example and the present example, can be used in two ways: either using the masses as unknowns or using the amounts of substance as unknowns. This choice is not innocent, as the outcome can be strikingly different. This cannot be only explained in terms of the lack of orthogonality in the conditions, because the two matrices and have the same condition number (59). The symbolic solutions to the problem are when solving for masses, and when solving for the amounts of substances. It is apparent that, for element , the precision is decreased to only 2 figures and, either rounding at the end or retaining the number of significant figures at each step, the value results 24 g. On the contrary, has three significant digits, therefore the resulting mass is 23.9 g. Another view on this behaviour can be obtained from the graphic form as we have done in paragraph 1.1: in Figure 2, we have plotted the reconstructed composition of the mixture for increased total mass of the mixture while keeping constant the amount of lead. The slope in the right panel is much larger than in the left one. Therefore, for a smaller variation in the input data, a larger error is obtained in the output.