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CHAPTER 2

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. SI MEASUREMENT. SI MEASUREMENT .

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CHAPTER 2

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  1. CHAPTER 2 ANALYZING DATA

  2. 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.

  3. SI MEASUREMENT

  4. SI MEASUREMENT

  5. SI MEASUREMENT • Prefixes are added to the base units to represent larger or smaller quantities. • Table 2.2: SI Prefixes, pg. 33 • MUST MEMORIZE

  6. SI MEASUREMENT

  7. 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

  8. DERIVED UNITS • 1) Derived SI units:combinations of SI base units Examples: density = mass volume

  9. 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

  10. 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.

  11. 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

  12. 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 = - )

  13. 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

  14. Dimensional Analysis • The “Factor-Label” Method • Units, or “labels” are canceled, or “factored” out

  15. 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.

  16. Dimensional Analysis • Lining up conversion factors: = 1 1 in = 2.54 cm 2.54 cm 2.54 cm 1 = 1 in = 2.54 cm 1 in 1 in

  17. qt mL  Dimensional Analysis • How many milliliters are in 1.00 quart of milk? 1 L 1.057 qt 1000 mL 1 L 1.00 qt = 946 mL

  18. lb cm3 Dimensional Analysis • You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. 1 cm3 19.3 g 1 kg 2.2 lb 1000 g 1 kg 1.5 lb = 35 cm3

  19. in3 L Dimensional Analysis • How many liters of water would fill a container that measures 75.0 in3? 1 L 1000 cm3 (2.54 cm)3 (1 in)3 75.0 in3 = 1.23 L

  20. cm in Dimensional Analysis 5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? 8.0 cm 1 in 2.54 cm = 3.2 in

  21. cm yd Dimensional Analysis 6) Taft football needs 550 cm for a 1st down. How many yards is this? 1 ft 12 in 1 yd 3 ft 1 in 2.54 cm 550 cm = 6.0 yd

  22. cm pieces Dimensional Analysis 7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? 1 piece 1.5 cm 100 cm 1 m 1.3 m = 86 pieces

  23. 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

  24. ERROR

  25. your value accepted value B. Percent Error • Indicates accuracy of a measurement

  26. % Error Problems • Try the two practice problems on the outline.

  27. Percent Error Examples • 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

  28. ERROR IN MEASUREMENT • In any measurement, some error or uncertainty exists • Measuring instruments themselves place limitations in precision • Estimate the final questionable digit.

  29. 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

  30. SIGNIFICANT FIGURES • Significant ≠ Certain • Must memorize the rules for recognizing significant figures!

  31. SIG. FIGS. RULES

  32. Atlantic-Pacific Check • Pacific, Atlantic, Decimal is Decimal is Present Absent

  33. Significant figures practice • Try the practice problems on the outline

  34. Sig. Figs. Practice • 804.05 g • 0.0144030 km • 1002 m • 400 mL • 30000. cm • 0.000625000 kg

  35. ROUNDING RULES

  36. 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 3.75 mL + 4.1 mL 7.85 mL  7.8 mL

  37. 3 SF 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 324g

  38. Sig. Figs./Rounding Practice • Try the practice problems on the outline.

  39. 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?

  40. Conversion Factors • Conversion factors are typically exact. • Do not count when determining # of significant figures in answer.

  41. y y x x E. Proportions • Direct Proportion • Inverse Proportion

  42. 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

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