Using Scientific Measurements SIGNIFICANT FIGURES AND SCIENTIFIC NOTATION

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Using Scientific Measurements SIGNIFICANT FIGURES AND SCIENTIFIC NOTATION

Using Scientific Measurements SIGNIFICANT FIGURES AND SCIENTIFIC NOTATION

Accuracy and Precision �Accuracy = closeness to the true value (bulls eye) �Precision =

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!

Percentage Error �Compares accuracy of experimental values with correct values �% error = experimental

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?

Error and Uncertainty in Measurement �Skill of measurer �Precision of instruments See figure 9

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?

Significant Figures �All the digits known with certainty plus one which is somewhat uncertain

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 #

Rounding �KNOW the rules for rounding! �Put them in your notes IN YOUR OWN

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!!)

Addition and Subtraction with Sig Figs �When adding or subtracting, the answer must have

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

Multiplication and Division with Sig Figs �The ans can have no more sig figs

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

Scientific Notation �Useful when writing very big or very little numbers �Expresses numbers in

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)

Mathematical Operations in Sci. Not. �Addition and subtraction: can only be performed if the

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 =

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

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