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Accuracy and Precision

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Early muzzle loading rifles did not have adjustable sights and so the marksman had to know how his particular gun performed and then how to compensate. In muzzle loading rifle competition it is precision that is rewarded. An X marks the spot where the three bullets should “group”.

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1234

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1234 High precision, but low accuracy

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1234 High precision, and high accuracy

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1234 Low precision, but high accuracy

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1234 Terrible precision, and lousy accuracy

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1234 Precision deals with reproducibility. The closer the data, the better the precision.

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1234 Accuracy is all about getting the right answer. The closer to the accepted value, the better the accuracy

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In science we not only want measurements which are accurate, but we want measurements which are precise. In experiments where there is little variation between measurements of the same thing, there is good precision.

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We judge the precision in measurements by the number of significant digits in the measurement.

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The greater the number of significant digits, the more reproducible the measurements are.

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We judge the precision in measurements by the number of significant digits in the measurement. The greater the number of significant digits, the more reproducible the measurements are. 1.304 cm is more precise and has more significant digits than 1.3 cm.

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When we do calculations, the answer can be no more precision than the least precise factor in the calculation. D = m/V D = 12.4837 g / 15.5 cm 3 D = ??? How precisely should we express the density?

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When we do calculations, the answer can be no more precision than the least precise factor in the calculation. D = m/V D = 12.4837 g / 15.5 cm 3 D = 0.8054 g/cm 3 0.8054 g/cm 3 has 4 significant digits, but the rules say that we can only have 3. 6 significant digits 3 significant digits

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When we do calculations, the answer can be no more precision than the least precise factor in the calculation. D = m/V D = 12.4837 g / 15.5 cm 3 D = 0.805 g/cm 3 We round the answer to 3 significant digits because 15.5 cm 3 has 3 significant digits, and it is the least precise factor. 6 significant digits 3 significant digits

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Mercury in a graduated cylinder. What is the volume? ??? The graduations are precise to +/- 1 cm 3. Therefore, no decimal places.

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Mercury in a graduated cylinder. What is the volume? 25 cm 3 The mass of the mercury is 338.25g. What is the value of the density?

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D = m / V D = 338.25 g / 25 cm 3 D = ??? 25 cm 3 How precisely can we express the density?

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D = m / V D = 338.25 g / 25 cm 3 D = 13.53 g/cm 3 25 cm 3 The calculator says 13.53. But! The answer can only be expressed to two significant digits.

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D = m / V D = 338.25 g / 25 cm 3 D = 14 g/cm 3 25 cm 3 Round the answer to two significant digits.

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Mike Jones Pisgah High School Canton NC 28721 mjones@haywood.k12.nc.us Last revised 04/04/12 C2012 – All rights reserved.

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