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STARTER

STARTER. The mass of an electron is : .000000000000000000000000000000911 kg. Put this number in scientific notation. Scientific Notation. If numbers are very large, like the mass of the Earth 5900000000000000000000000 kg. Or very small like the mass of an electron :

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STARTER

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

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

  3. Scientific Notation A number in scientific notation has two parts: 1st part: a number between 1 and 10 2nd part: 10 to some power. Example: 5.9 x 1024 1024 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.

  4. Examples – Put the number in Scientific Notation a. 345000 Answer: 345000 = 3.45 x 105 b. .00034 Answer: .00034 = 3.4 x 10-4

  5. 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 104 Press: 1.56(EE)4 Display: 1.56E4 In other words, E4 stands for “x 104 “

  6. Multiplication and Division

  7. Examples Simplify: (2 x 103)(4 x 106) = (2)(4) x 103(106) = 8 x 109 Simplify: (4 x 103)/(2 x 106) = (4)/(2) x 103/106= 2 x 10-3 Simplify: (2 x 103)3 = 23x (103 )3= 8 x 109

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

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

  10. 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

  11. Summary For decimal numbers, start from the left and find the 1st 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 1st 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

  12. 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 102

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

  14. Significant FiguresAfter 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

  15. 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

  16. Percent Error and Difference

  17. Accuracy vs. Precision

  18. 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

  19. 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 in2. So…… 94 in2 = __________cm2 94 in2(2.54cm/1 in)2 = 94(6.45 cm2) / (1 in2) = 606 cm2

  20. 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 ( 123 in3/ 13 ft3) = 1728in3

  21. Using S.I. Prefixes

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

  23. Examples Change 250 grams to kilograms. 1 kg = 1x103 gram 250g ( 1 kg/1x103 g) = .250 kg

  24. Example A metal plate is 12.0cm by 4.0cm. What is the area in square meters? Use the fact that c = x 10-2 Area = (12.0cm)(4.0cm) = (12.0x10-2m)(4.0 x 10-2 m) = 4.8 x 10-3m2

  25. 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?

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