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CHAPTER 2 ANALYZING DATA SI MEASUREMENT SI (def): Le Systeme International d’ Unites (International System of Units) SI has 7 base units and almost all other units are derived from these. SI MEASUREMENT QUANTITY QUANTITY SYMBOL UNIT NAME UNIT ABBREVIATION Length l meter m (not italicized) Mass m (italicized) kilogram kg Time t second s Temperature T Kelvin K SI MEASUREMENT QUANTITY QUANTITY SYMBOL UNIT NAME UNIT ABBREVIATION Amount of substance n mole mol Electric current I ampere A Luminous intensity IV candela cd SI MEASUREMENT Prefixes are added to the base units to represent larger or smaller quantities. Table 2.2: SI Prefixes, pg. 33 MUST MEMORIZE SI MEASUREMENT SI MEASUREMENT SI units are defined in terms of standards of measurement. They are either objects or consistent natural phenomena. International organizations monitor the defining process. In the US, the National Institute of Standards and Technology plays a major role in setting standards DERIVED UNITS 1) Derived SI units: combinations of SI base units Examples: density = mass volume DERIVED UNITS 2) volume: amount of space occupied by an object non-SI volume unit: liter, L 1 L = 1000 cm3 SI volume unit: m3 DERIVED UNITS 3) density: mass per unit volume d = m/V Mass and volume change proportionately, meaning that the ratio of m to V is constant. Density is an intensive property. Density and temperature: at high T, most objects expand. SCIENTIFIC NOTATION Scientific Notation: numbers written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10, and n is a whole number. 65 000 km 6.5 x 104 km 0.0012 mm 1.2 x 10-3 mm Scientific Notation Rules To find M: Move the decimal point in the original # to the left or right so that only one nonzero digit remains to the left of the decimal point To find n: Count the # of places that you moved the decimal point (Moved left, n = + Moved right, n = - ) SCIENTIFIC NOTATION Addition and Subtraction: Values must have same value exponent before you can do these operations Multiplication: M factors are multiplied and exponents are added Division: M factors divided and exponent of denominator subtracted from exponent of numerator Dimensional Analysis The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out cm 3 g cm 3 g Dimensional Analysis Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer. Dimensional Analysis Lining up conversion factors: 1 in = 2.54 cm =1 2.54 cm 2.54 cm 1 in = 2.54 cm 1= 1 in 1 in Dimensional Analysis How many milliliters are in 1.00 quart of milk? qt mL 1.00 qt 1L 1000 mL 1.057 qt 1L = 946 mL Dimensional Analysis You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. cm3 lb 1.5 lb 1 kg 1000 g 1 cm3 2.2 lb 1 kg 19.3 g = 35 cm3 Dimensional Analysis How many liters of water would fill a container that measures 75.0 in3? in3 L 75.0 in3 (2.54 cm)3 (1 in)3 1L 1000 cm3 = 1.23 L Dimensional Analysis 5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? cm in 8.0 cm 1 in 2.54 cm = 3.2 in Dimensional Analysis 6) Taft football needs 550 cm for a 1st down. How many yards is this? cm 550 cm yd 1 in 1 ft 1 yd 2.54 cm 12 in 3 ft = 6.0 yd Dimensional Analysis 7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? cm pieces 1.3 m 100 cm 1m 1 piece 1.5 cm = 86 pieces A. Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT ERROR B. Percent Error Indicates accuracy of a measurement % error experiment al literature literature your value accepted value 100 % Error Problems Try the two practice problems on the outline. Percent Error Examples a. What is the % error for a mass measurement of 17.7 g if the correct value is 21.2 g? 17.7 g – 21.2 g x 100 = 21.2 g b. A volume is measured experimentally to be 4.26 mL. What is the % error if the correct value is 4.15 mL? 4.26 mL – 4.15 mL x 100 = 4.15 mL ERROR IN MEASUREMENT In any measurement, some error or uncertainty exists Measuring instruments themselves place limitations in precision Estimate the final questionable digit. D. Significant Figures Indicate precision of a measurement. Recording Sig Figs – Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm SIGNIFICANT FIGURES Significant ≠ Certain Must memorize the rules for recognizing significant figures! SIG. FIGS. RULES RULE EXAMPLE 1. No zeros, All sig. 852 m 97.25 mL 2. Zeros between nonzero digits = sig. 3. Zeros at front of nonzero digits ≠ sig. 40.7 L 87009 km 0.095897 m 0.0009 kg 4. Zeros at end of # and 85.00 g to right of decimal = sig. 9.000 000 000 mm 5. Decimal after zeros, 2000 m sig. Zeros with no 2000. m Atlantic-Pacific Check Pacific, Decimal is Present Atlantic, Decimal is Absent Significant figures practice Try the practice problems on the outline Sig. Figs. Practice a) 804.05 g b) 0.0144030 km c) 1002 m d) 400 mL e) 30000. cm f) 0.000625000 kg ROUNDING RULES Digit after last digit Last digit should: to be kept: Examples (3 sig. Figs) >5 Increase by 1 42.68 g 42.7 g <5 Stay the same 17.32 m 17.3 m 5, followed by nonzero 5, preceded by odd 5, preceded by even Increase by 1 2.7851 cm 2.79 cm 4.635 kg 4.64 kg 78.65 mL 78.6 mL Increase by 1 Stay the same C. Significant Figures Calculating with Sig Figs (con’t) – Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 7.85 mL 7.8 mL C. Significant Figures Calculating with Sig Figs – Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 3 SF 324 g Sig. Figs./Rounding Practice Try the practice problems on the outline. Practice Problems 1. What is the sum of 2.099 and 0.05681? 2. Calculate the quantity 87.3 cm – 1.655 cm 3. Polycarbonate has a density of 1.2 g/cm3. A photo frame is constructed from two 3.0 mm sheets. Each side measures 28 cm by 22 cm. What is the mass of the frame? Conversion Factors Conversion factors are typically exact. Do not count when determining # of significant figures in answer. E. Proportions Direct Proportion y x y x Inverse Proportion y 1 y x x Direct and Indirect Proportions Direct: 2 quantities are directly proportional if dividing one by the other gives a constant value; graph is a straight line, y/x = k Indirect: 2 quantities are indirectly proportional if their product is constant, graph curved, xy = k or y α 1/x GRAPHS