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Chapter 2 “Scientific Measurement” Standards for Measurement Accuracy vs. Precision Significant Figures

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International System of Units 1. Measurements depend upon units that serve as reference standards 2. The standards of measurement used in science are those of the Metric System

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The Fundamental SI Units (Le Système International, SI)

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3. All other measurements are derived (or calculated) from the measurements in the SI System. 4. The following are some derived units used in science. VolumeAny cubic unit of length AreaAny square unit of length DensityAny mass unit per volume VelocityAny unit of length per time ConcentrationAny unit of mass per volume All derived units are based on using a formula. Example :volume = (L)(W)(H)

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Accuracy vs. Precision 5. It is necessary to make good, reliable measurements in the lab 6. Accuracy – how close a measurement is to the true value 7. Precision – how close the measurements are to each other (repeatability)

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a. Precision also reflects the number of decimal places in a measurement. For example: 2.500 grams is more precise than 2.5 grams.

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Precision and Accuracy Neither accurate nor precise Precise, but not accurate Precise AND accurate

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Example: Technician A and B measured the density of a substance several times. The actual density is 2.70 g/ml. Which technician was more precise and which was more accurate and why? Tech ATech B 2.000 g/ml2.5 g/ml 1.999 g/ml2.9 g/ml 2.001 g/ml2.7 g/ml

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Accuracy, Precision, and Error 8. Accepted value = the correct value based on reliable references (you can look this one up) 9. Experimental value = the value measured in the lab (you came up with this in lab)

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Accuracy, Precision, and Error 10. Error = accepted value – exp. value Can be positive or negative 11. Percent error = the absolute value of the error divided by the accepted value, then multiplied by 100% | accepted value – exp. value | accepted value x 100% error =

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Significant Figures in Measurements 12. Significant figures in a measurement include all of the digits that are known, plus one more digit that is estimated. 13. Measurements must be reported to the correct number of significant figures.

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Figure 3.5 Significant Figures: Which measurement is the best? What is the measured value?

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Reading for graduated cylinders Read at the bottom of the meniscus. Include one more digit than the smallest division. Reading = 35.0 mls not 35 mls

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Rules for Counting Significant Figures Non-zeros always count as significant figures: 1. Non-zeros always count as significant figures: 3456 has 4 significant figures

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Rules for Counting Significant Figures 2. Leading zeroes do not count as significant figures: 0.0486 has 3 significant figures

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Rules for Counting Significant Figures 3. Captive zeroes always count as significant figures: 16.07 has 4 significant figures

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Rules for Counting Significant Figures 4. Trailing zeros (or zeros after a non- zero digit) are significant only if the number contains a written decimal point: 9.300 has 4 significant figures 100 has 1 significant figure 100.0 has 4 significant figures

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Sig Fig Practice #1 How many significant figures in the following? 1.0070 m 5 sig figs 17.10 kg 4 sig figs 100,890 L 5 sig figs 3.29 x 10 3 s 3 sig figs 0.0054 cm 2 sig figs 3,200,000 mL 2 sig figs These all come from some measurements

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