SigFig%20and%20Measure%20%28IP%29

# SigFig%20and%20Measure%20%28IP%29 - Significant Figures and...

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1 1 Significant Figures and Measurement Carl Hoeger University of California, San Diego Significant Figures and Measurement SigFig-2 Measurements • Science is about making observations and measurements; how do we convey to someone just HOW good/sure of our data we are? • All quantitative measurements are made using some sort of device (analog or digital). Need value, units, and error. • All data collection has errors associated with it: Determinate Errors : aka systematic errors ; have a definite direction and magnitude and have an assignable cause. Indeterminate Errors : aka random errors or noise ; errors that simply arise from uncertainties in a measurement, sloppy techniques, anomalous physical and environmental factors; these errors are typically untraceable. Determinate errors can be eliminated; Indeterminate errors can not.

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2 Significant Figures and Measurement SigFig-3 Measurements (cont.) • Consider the measurement of a length of bar: • Is it 8.3, 8.32, or 8.323? Or 8.322? What are the units? Error? Depends! • Calibration • Multiple measurements to give means and standard deviations: ( ) ; ; 100 –1 i i x x x s x s CV x N N = = = ! " " Significant Figures and Measurement SigFig-4 Accuracy and Precision Accuracy : closeness of measurement to the true value Precision : closeness of individual measurements to one another
3 Significant Figures and Measurement SigFig-5 Significant Figures-1 Two types of numbers exist: measured and exact numbers. • Measurements or “determined” values contain significant figures and must convey to the reader the ‘certainty’ of your measurement. This is where significant figures (SigFigs) comes in. • Exact values (exact numbers) have an unlimited number of significant figures and never detract from a measurement or its subsequent modification or use. Significant Figures and Measurement SigFig-6 Exact Values Exact numbers can either be cardinal (counted) or defined . • Cardinal or counted values represent values that, by their very nature or how they are obtained, are indivisible without destroying the identity of the unit. 10 dogs or 85 cars; 123 molecules; 13 silver atoms; 2500 electrons; 2 chloride ions in 1 calcium chloride. • Defined values are those for which the value has been exactly defined. “1” in these expressions is EXACTLY 1 1 in = 2.54 cm; 1000 m = 1 km; 1 mg = 0.001 g; 1 lb = 16 oz All metric to metric or english to english conversions • What about constants? c = 2.998 x 10 8 m/sec?

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4 Significant Figures and Measurement SigFig-7 Measured Values • Determined values have SigFigs associated with them. • Reported values must convey the level of precision of the measurement to a detached third-party (i.e. an unseen colleague). • A measured value is comprised of digits we know for certain
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SigFig%20and%20Measure%20%28IP%29 - Significant Figures and...

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