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Reliability of Measurements Chapter 2.3

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Objectives I can define and compare accuracy and precision. I can calculate percent error to describe the accuracy of experimental data. I can use significant figures and rounding to reflect the certainty of data.

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Accuracy and Precision Often accuracy and precision confused for one another, but they are different concepts. ACCURACY How close the measured value is to the accepted value Ex: How close to the center of the dart board? PRECISION How close a series of measurements are to one another Ex: How close together are all the darts you throw together? If you took another measurement, how close would it be to the others?

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Accuracy and Precision What are the precision and accuracy levels of the following? Low Accuracy High Accuracy Low Accuracy High Precision High Precision Low Precision

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Whose data is most accurate/precise? Three chemistry students measured the mass and volume of a piece of zinc to determine it’s density. The table below shows the data: JohnSamSara Trial 17.17 g/mL7.65 g/mL7.04 g/mL Trial 27.14 g/mL7.65 g/mL7.55 g/mL Trial 37.13 g/mL7.64 g/mL7.26 g/mL Average7.15 g/mL7.65 g/mL7.28 g/mL Compare the students data. Whose data is the most accurate and precise?

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Percent Error A way to evaluate the accuracy of data. Percent Error=Ratio of the error to the accepted value │ Accepted value – Measured value │ Accepted value X 100%

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Percent Error If your measurement of a liquid is 123.4 mL but the actual amount is 125.0 mL, what is the percent error of the measurement? 125.0 mL – 123.4 mL 1.6 mL ________________________________________ _______________ 125.0 mL 125.0 mL = X 100% = 1.3%

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Percent Deviation A way to evaluate the precision of the data. Percent Deviation=Ratio of your measurements change from the average compared to the average value │ Mean value – Measured value │ Mean value X 100%

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Percent Deviation If one of your measurements of the length of a string was 22.7 cm and the mean measurement was 22.9 cm, what is the percent deviation of the measurement? 22.9 cm – 22.7 cm 0.2 cm ________________________________________ _______________ 22.9 cm 22.9 cm = X 100% = 0.9%

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Significant Figures The number of digits reported in a measurement. All the known digits plus one estimated value. The number of significant figures possible depends upon the piece of equipment used to take the measurement.

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Significant Figures

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Rules for Significant Figures 1.Non-zero numbers are always significant. 2.Zeros between non-zeros are always significant. 3.All final zeros to the right of the decimal place are significant. 4.Zeros that act as placeholders are NOT significant. 5.Counting numbers and defined constants have an infinite number of significant figures.

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Practicing Significant Figures Determine the number of sig figs in the following numbers. 1)0.02 2)70001 3)5600 4)4.100 5)3.1416 (π) 6)2.80 x 10 5 0.02 70001 5600 4.100 3.1416 (π) 2.80 x 10 5 1 5 2 4 Infinite 3 Red numbers=significant Black numbers=not significant

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Rules for Rounding If the digit to the immediate right of the last sig fig is 5-9, round up. If not, leave as is.

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Significant Figures and Calculators When using a calculator, you should do the calculation using the digits allowed by the calculator and round off only at the end of the problem. Do not round off in the middle of the problem!

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Sig Figs and Addition/Subtraction + - + - + - + - + - + - + - + When you add or subtract, you answer must have the same number of digits to the right of the decimal point as the original value with the fewest digits to the right of the decimal place. + - + - + - + - + - + - + - +

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Sig Figs and Multiplication/Division When you multiply or divide, your ansere must have the same number of significant figures as the original value with the least significant figures.

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Practicing Significant Figures 3.33 m 2 25 m 53 mL 26.6 g 6.7 cm 3

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