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STARTER The mass of an electron is :.000000000000000000000000000000911 kg The mass of an electron is :.000000000000000000000000000000911 kg Put this number in scientific notation.

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Scientific Notation If numbers are very large, like the mass of the Earth 5900000000000000000000000 kg If numbers are very large, like the mass of the Earth 5900000000000000000000000 kg Or very small like the mass of an electron :.000000000000000000000000000000911 kg Or very small like the mass of an electron :.000000000000000000000000000000911 kg then standard decimal notation is very cumbersome, so we use scientific notation.

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Scientific Notation A number in scientific notation has two parts: 1 st part: a number between 1 and 10 2 nd part: 10 to some power. A number in scientific notation has two parts: 1 st part: a number between 1 and 10 2 nd part: 10 to some power. Example: 5.9 x 10 24 10 24 Means move the decimal 24 places to the right. Example: 6.2 x 10 -4 10 -4 Means move the decimal 4 places to the left.

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Examples – Put the number in Scientific Notation a. 345000 b..00034 Answer: 345000 = 3.45 x 10 5 Answer:.00034 = 3.4 x 10 -4

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Calculators To enter a number in scientific notation into a calculator, the most common method is to use the EE button. Example: to enter 1.56 x 10 4 Press: 1.56(EE)4 Display: 1.56E4 In other words, E4 stands for “x 10 4 “ To enter a number in scientific notation into a calculator, the most common method is to use the EE button. Example: to enter 1.56 x 10 4 Press: 1.56(EE)4 Display: 1.56E4 In other words, E4 stands for “x 10 4 “

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Multiplication and Division RuleExample x m x n = x m+n x 2 x 3 = x 2+3 = x 5 x m /x n = x m-n x 6 /x 2 = x 6-2 = x 4 (x m ) n = x mn (x 2 ) 3 = x 2×3 = x 6 (xy) n = x n y n (xy) 3 = x 3 y 3 (x/y) n = x n /y n (x/y) 2 = x 2 / y 2 x -n = 1/x n x -3 = 1/x 3

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Examples Simplify: (2 x 10 3 )(4 x 10 6 ) = (2)(4) x 10 3 (10 6 ) = 8 x 10 9 Simplify: (4 x 10 3 )/(2 x 10 6 ) = (4)/(2) x 10 3/ 10 6 = 2 x 10 -3 Simplify: (2 x 10 3 ) 3 = 2 3 x (10 3 ) 3 = 8 x 10 9

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Significant Figures How to count the number of significant figures in a decimal number. How to count the number of significant figures in a decimal number. Zeros Between other non-zero digits are significant. a. 50.3 has three significant figures b. 3.0025 has five significant figures

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Significant Figures Zeros in front of nonzero digits are not significant: 0.892 has three significant figures 0.0008 has one significant figure

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Significant Figures Zeros that are at the end of a decimal number are significant. 57.00 has four significant figures 2.000000 has seven significant figures At the end of a non-decimal number they are not. 5700 has two significant figures 2020 has three significant figures

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Summary For decimal numbers, start from the left and find the 1 st nonzero digit. This digit and all others to the right are counted. 002.3400 has 5 sig. figs. For non-decimals, start from the left and find the 1 st nonzero digit. This digit and all others to the right are counted until you get to only zeros which are not counted. 02304500 has 5 sig. figs For decimal numbers, start from the left and find the 1 st nonzero digit. This digit and all others to the right are counted. 002.3400 has 5 sig. figs. For non-decimals, start from the left and find the 1 st nonzero digit. This digit and all others to the right are counted until you get to only zeros which are not counted. 02304500 has 5 sig. figs

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Non-Decimal Numbers Major pain to try to figure out the significant figures – it depends on the number’s history. Don’t Use Them. Use Scientific Notation to express any number to a desired amount of significant figures. Example: Express 234 to 4 sig. figs. 2.340 x 10 2

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Practice Find the number of significant figures. 1. 2.00450 2..0034050 3. 1450 4. 0.02040 1. 6 sf’s. 2. 5 sf’s 3. 3 sf’s 4. 4 sf’s 1. 6 sf’s. 2. 5 sf’s 3. 3 sf’s 4. 4 sf’s

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Significant Figures After Division and Multiplication After performing the calculation, note the factor that has the least number of sig figs. Round the product or quotient to this number of digits. 3.22 X 2.1 = 6.762 6.8 36.5/3.414 = 10.691 10.7

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Significant Figures Addition or subtraction with significant figures: – The final answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal. Ex: 97.3 + 5.85 = 103.15 103.2

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Percent Error and Difference

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Accuracy vs. Precision

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Conversions Converting From One System of Units to Another You will need a conversion factor like ( 1 meter = 3.28 ft). It can be used two ways: (1m/3.28ft) or ( 3.28ft/1m) Multiply your given dimension by the conversion factor to obtain the desired dimension. How many feet in 2 meters? 2m (3.28ft/m) = 6.56 feet How many meters in 10 feet? 10ft(1m/3.28ft) = 3.05 meters

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Converting Areas To convert areas, you must square the conversion factor. Conversion factor: 1 inch = 2.54cm A page is 8.5 inches by 11 inches. What is the area in square centimeters? The area in square inches is 94 in 2. So…… 94 in 2 = __________cm 2 94 in 2 (2.54cm/1 in) 2 = 94(6.45 cm 2 ) / (1 in 2 ) = 606 cm 2

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Converting Volumes To convert volumes, you must cube the conversion factor. A cubic foot is how many cubic inches? Conversion factor: 1 foot = 12 inches 1 ft 3 ( 12 in/ 1 ft) 3 = 1 ft 3 ( 12 3 in 3 / 1 3 ft 3 ) = 1728in 3

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Using S.I. Prefixes

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Examples Change 12nm to meters. n = x 10 -9 so replace it: Change 12nm to meters. n = x 10 -9 so replace it: 12nm = 12 x 10 -9 m Finished.

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Examples Change 250 grams to kilograms. 1 kg = 1x10 3 gram Change 250 grams to kilograms. 1 kg = 1x10 3 gram 250g ( 1 kg/1x10 3 g) =.250 kg

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Example A metal plate is 12.0cm by 4.0cm. What is the area in square meters? Area = (12.0cm)(4.0cm) = (12.0x10 -2 m)(4.0 x 10 -2 m) = 4.8 x 10 -3 m 2 Use the fact that c = x 10 -2

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Exit Physics uses the S.I. metric system, also known as the “mks” system. In this system, what are the base units for mass, time, and length? Physics uses the S.I. metric system, also known as the “mks” system. In this system, what are the base units for mass, time, and length?

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