Analysis_Methodology_PLS

Analysis_Methodology_PLS - Department of Mechanical...

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Department of Mechanical Engineering Analysis Methodology ES 140 Section 5 Fall 2006
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Department of Mechanical Engineering Details of Analysis Scientific notation Significant figures Precision Results validation Computer usage
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Department of Mechanical Engineering Scientific notation Scientists and engineers need a compact way to express both very large and very small numbers. Scientific notation is used for this. Numbers are expressed as the product of a number and a power of 10. Examples: 123,000,000 = 1.23×10 8 0.000028 = 2.8×10 -5
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Department of Mechanical Engineering Engineering Notation Engineers typically group by powers of 3 to get numbers in the format most convenient for use. Engineers don’t say 0.3 m, we use 300 mm. We don’t use 1,250 W, we use 1.25kW. Young’s modulus for steel is 30x10 6 psi. Metric prefixes are not commonly used with English units. This is the way that manufacturers format the data they provide for your use, and the way it is quoted in Handbooks.
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Department of Mechanical Engineering Significant Figures The significant figures of a number are the digits from the first nonzero digit on the left to either: the last digit (zero or nonzero) on the right if there is a decimal point, or the last nonzero digit of the number if there is no decimal point
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Department of Mechanical Engineering How many significant figures? (a) 2300 or 2.3×10 3 (b) 2300. or 2.300×10 3 (c) 2300.0 or 2.3000×10 3 (d) 23,040 or 2.304×10 4 (e) 0.035 or 3.5×10 -2 -2
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Department of Mechanical Engineering Numerical Precision The number of significant figures provides an indication of the precision with which the quantity is known. Generally, the last significant figures may be off by as much as a half-unit. E.g. Writing mass = 8.3 g (2 significant figures), the mass lies somewhere between 8.25 and 8.35 g Whereas mass = 8.300 g (4 significant figures), the mass lies between 8.2995 and 8.3005 g This applies only to measured quantities and numbers calculated from measured quantities (for counted values, e.g. 3 balloons, the 3 is exact and is the same as 3.0 or 3.000 balloons).
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Department of Mechanical Engineering Precision of Calculations Rules for multiplication and division: The correct number of significant figures in the result equals the lowest number of significant figures
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Analysis_Methodology_PLS - Department of Mechanical...

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