Chapter 2 Data Analysis

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

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

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

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

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

Scientific Notation and 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

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

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

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

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

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

How Reliable are Measurements? Significant Figures Rule Examples Non-zero numbers are always significant 72.3 g has 3 Zeros between non-zero numbers are always significant 40.7 L has 3 87009 has 5 All final zeros to the right of the decimal place are significant 6.20 g has 3 Zeros that act as placeholders are NOT significant. Convert to scientific notation. 0.0253 g has 3 2000 m has 1 Constants and counting numbers have infinite number of significant figures. 6 molecules 60 s = 1 min

How Reliable are Measurements? Rounding off numbers Rule Example Digit to immediate right of last significant figure <5, do not change the last significant figure. 2.5322.53 Digit to immediate right of last significant figure >5, round up the last significant figure 2.5362.54 Digit to immediate right of last significant figure = 5 AND followed by a nonzero digit, round up last significant figure. 2.5351--.2.54 Digit to immediate right of last significant figure = 5 AND is not followed by a nonzero digit, look at last significant figure. If it is an odd digit, round it up; if it is an even digit, round it down. 2.53502.54 2.52502.52

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

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

Representing Data Graphing Circle graphs Bar graph 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

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

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