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SIGNIFICANT FIGURES AND SCIENTIFIC NOTATION Using Scientific Measurements

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Accuracy and Precision Accuracy = closeness to the true value (bulls eye) Precision = repeatability of measurements (closeness to other darts thrown) It is important to strive to be accurate AND precise!

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Percentage Error Compares accuracy of experimental values with correct values % error = experimental value – accepted value X 100 accepted value Ex. I give you a sample of copper, you measure the density and get 9.0 g/cm 3. The accepted value for the density of copper is 8.92 g/cm 3. What is the % error?

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Error and Uncertainty in Measurement Skill of measurer Precision of instruments See figure 9 page 46, read 1 st 2 paragraphs on page What’s going on here?

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Significant Figures All the digits known with certainty plus one which is somewhat uncertain or is estimated. See table 5 KNOW THESE RULES!!!! All measurements and math problem answers in this class must be reported using these rules! DO NOT COPY the rules. Shorten them into your own words in your notes NOW. Ex. 1. all non-zero # 2. zeros btw non-zero #

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Rounding KNOW the rules for rounding! Put them in your notes IN YOUR OWN WORDS and shortened down (you have 5 minutes, DO NOT COPY!!)

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Addition and Subtraction with Sig Figs When adding or subtracting, the answer must have the same # of sig figs to the right of the decimal as the original # with the fewest # of sig figs to the right of the decimal. Ex. 5.44 - 2.6103 = 2.8297, but you report it as 2.83 When working with whole numbers, the answer must have the same # of sig figs as the original number with the fewest # of sig figs. Ex. 5400 + 365 = 5765, but you report it as 5800

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Multiplication and Division with Sig Figs The ans can have no more sig figs than are in the original # with the fewest sig figs. Ex. 3.05/8.47 = 0.360094451, but report as 0.360 Ex. 45.9 x 16003 = 734537.7, but report as 73.5

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Scientific Notation Useful when writing very big or very little numbers Expresses numbers in the form M x 10 n for #>0, n will be (+) for #<0, n will be (-) e.g. (for example)

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Mathematical Operations in Sci. Not. Addition and subtraction: can only be performed if the values have the same exponent (n) If the n values are not =, you have to make them =

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Multiplication: numbers (M) are multiplied, exponents (n) are added Division: numbers (M) are divided, exponents (n) are subtracted

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