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Chapter 2

Chapter 2. Data Analysis. Units of Measurement. Measurement Comparison to a standard Standard Well defined Make consistent measurements Useful measurement Number Unit SI Units Système Internationale d’Unités —SI Standard unit of measure. Units of Measurement. Base units

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Chapter 2

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  1. Chapter 2 Data Analysis

  2. Units of Measurement • Measurement • Comparison to a standard • Standard • Well defined • Make consistent measurements • Useful measurement • Number • Unit • SI Units • SystèmeInternationaled’Unités—SI • Standard unit of measure

  3. Units of Measurement • Base units • 7 base units (p. 26 Table 2-1) • Defined unit • Based on object or event in physical world • Independent of other units • Time • Frequency of microwave radiation given off by cesium-133 atom • Second, s • Length • Distance light travels through a vacuum in 1/299792458 of a second. • Meter, m • Mass • Defined by the platinum-iridium metal cylinder • Kilogram, kg • Volume • Measure of the amount of a liquid • Liter, L

  4. Units of Measurement • Prefixes • Table p. 26 • mega- micro • hecto (h_): 102 • deka (da_ or dk_): 10 • decimeter • 1 dm = .1 m • 10 cm = 1 dm • 1000 cm3 = 1 dm3 • King Henry Died By Drinking Chocolate Milk • Yotta (Y_): 1024 • 1 septillion • Yocto (y_): 10-24 • 1 septillionth

  5. Units of Measurement • Derived Units • Require a combination of base units • Volume • L X W X H • 1 cm3 = 1 mL = 1 cc • Density • mass/volume • DH2O = 1.00 g/mL • D = m/v • M = DV • V = M/D • Practice p. 29 #1-3; p. 30 #4-11; p. 50 #51-57

  6. Units of Measurement • Temperature • Measure of how hot or cold an object is relative to other objects • kelvin, K • Water • freezes about 273 K • boils about 373 K

  7. Scientific Notation and Dimensional Analysis • Scientific notation expresses numbers as: • M x 10n • M is a number between 1 & 10 • Ten raised to a power (exponent) • n is an integer • Adding & subtracting • Exponents must be the same • Multiplying & dividing • Multiply or divide first factors • Add exponents for multiplication • Subtract exponents for division • Practice Problems p. 32 #12-16; p. 50 #75-78

  8. Scientific Notation and Dimensional Analysis • Dimensional analysis • Solving problems with conversion factors • Conversion factor • Ration based on an equality • Ex. 12 in./1 ft. or 1 ft./12 in. • Ex. 7 days/1 wk • Focuses on units used 48 km =? m (48 km)X (1000 m/1km) = 48,000 m

  9. Scientific Notation and Dimensional Analysis What is a speed of 550 m/s in km/min? • Practice Problems p. 35 #19-28; p. 51 #79-80

  10. How Reliable are Measurements? Accuracy and Precision • Accuracy • The nearness of a measurement to its accepted value • Precision • The agreement between numerical values of two or more measurements that have been made in the same way. • You can be precise without being accurate. • Systematic errors can cause results to be precise but not accurate

  11. How Reliable are Measurements? Accuracy and Precision • Percent error • Compares the size of an error to the size of the accepted value • Calculating Percent Error (Relative Error) • Percent error = error X 100 Value Accepted • Error = Value Accepted – Value Experimental • Take the absolute difference • Ignore if positive or negative integer

  12. How Reliable are Measurements? • Error in Measurement • Some error or uncertainty exists in all measurement • No measurement is known to an infinite number of decimal places. • All measurements should include every digit known with certainty plus the first digit that is uncertain • Practice Problems p. 38 #29-30; p. 51 #81-82

  13. How Reliable are Measurements? • Significant Figures • Represent measurements • Include digits that are known • One digit is estimated

  14. How Reliable are Measurements? Significant Figures

  15. How Reliable are Measurements? • Rounding off numbers

  16. How Reliable are Measurements? • Rounding off numbers • Addition and subtraction • Answer must have same number of digits to right of the decimal place as value with fewest digits to the right of the decimal point. • Example: 1.24 mL 12.4 mL + 124 mL 137.64 mL = 138 mL

  17. How Reliable are Measurements? • Rounding off numbers • Multiplication and division • Answer must have same number of significant figures as the measurement with the fewest significant figures • Practice problems: p. 39 #31-32; p. 41 #33-36; p. 42 #37-44; p. 51 #83-85

  18. Representing Data • Graphing • Circle graphs • Also called pie chart • Show parts of a fixed whole, usually percents • Bar graph • Show how a quantity varies with factors • Ex. Time, location, temperature • Measured quantity on y-axis (vertical axis) • Independent variable on x-axis (horizontal axis) • Heights show how quantity varies

  19. Representing Data • Line Graphs • Points represent intersection of data for two variables • Independent variable on x-axis • Dependent variable on y-axis • Best fit line • Equal points above and below line • Straight line—variables directly related • Rises to the right—positive slope • Sinks to the right—negative slope • Slope = y2-y1 = Δy x2-x1 Δx

  20. Representing Data • Interpreting Graphs • Identify independent and dependent variables • Look at ranges of data • Consider what measurements were taken • Decide if relationship is linear or nonlinear • Practice problems p. 51-52 #86-87

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