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Chapter 3

Chapter 3. Scientific measurement. Types of measurement. Quantitative - (quantity) use numbers to describe Qualitative - (quality) use description without numbers 4 meters extra large Hot 100ºC. Quantitative. Qualitative. Qualitative. Quantitative.

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Chapter 3

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  1. Chapter 3 Scientific measurement

  2. Types of measurement • Quantitative- (quantity) use numbers to describe • Qualitative- (quality) use description without numbers • 4 meters • extra large • Hot • 100ºC Quantitative Qualitative Qualitative Quantitative

  3. Which do you Think Scientists would prefer • Quantitative- easy check • Easy to agree upon, no personal bias • The measuring instrument limits how good the measurement is

  4. How good are the measurements? • Scientists use two word to describe how good the measurements are • Accuracy- how close the measurement is to the actual value • Precision- how well can the measurement be repeated

  5. Differences • Accuracy can be true of an individual measurement or the average of several • Precision requires several measurements before anything can be said about it • examples

  6. Let’s use a golf anaolgy

  7. Accurate? No Precise? Yes

  8. Accurate? Yes Precise? Yes

  9. Precise? No Accurate? NO

  10. Accurate? Yes Precise? We cant say!

  11. Reporting Error in Experiment • Error • A measurement of how accurate an experimental value is • (Equation) Experimental Value – Accepted Value • Experimental Value is what you get in the lab • accepted value is the true or “real” value • Answer may be positive or negative

  12. Reporting Error in Experiment • % Error = • | experimental – accepted value | x 100 • accepted value • OR | error| x 100 • accepted value • Answer is always positive

  13. Example: A student performs an experiment and recovers 10.50g of NaCl product. The amount they should of collected was 12.22g on NaCl. • Calculate Error • Error = 10.50 g - 12.22 g • = - 1.72 g • Calculate % Error • % Error = | -1.72g | x 100 • 12.22g • = 14.08% error

  14. Scientific Notation Example: 2.5x10-4 (___) is the coefficient and ( ___) is the power of ten 2.5 -4 Convert to Scientific Notation And Vise Versa 5500000 = ____________ 3.44 x 10-2 = ____________ 2.16 x 103 = ____________ 0.00175 = ____________ 5.5 x 106 0.0344 2160 1.75 x 10-3

  15. Multiplying and Dividing Exponents using a calculator (3.0 x 105) x (3.0 x 10-3) = _________________ (2.75 x 108) x (9.0 x 108) = ________________ (5.50 x 10-2) x (1.89 x 10-23) = ____________ (8.0 x 108) / (4.0 x 10-2) = ________________ 9.00 x 102 2.475 x 1017 1.04 x 10-24 2.0 x 1010

  16. Adding and Subtracting Exponents using a calculator 2.575 x 109 7.5 x 107 + 2.5 x 109 = __________________ 5.5 x 10-2 - 2.5 x 10-5 = _________________ 5.498 x 10-2

  17. 1 2 3 4 5 Significant figures (sig figs) • How many numbers mean anything • When we measure something, we can (and do) always estimate between the smallest marks. 4.5 inches

  18. Significant figures (sig figs) • Scientist always understand that the last number measured is actually an estimate 4.56 inches 1 2 3 4 5

  19. Sig Figs • What is the smallest mark on the ruler that measures 142.15 cm? • 142 cm? • 140 cm? • Here there’s a problem does the zero count or not? • They needed a set of rules to decide which zeroes count. • All other numbers do count Tenths place Ones place Yikes!

  20. Which zeros count? • Those at the end of a number before the decimal point don’t count • 12400 • If the number is smaller than one, zeroes before the first number don’t count • 0.045 = 3 sig figs = 2 sig figs

  21. Which zeros count? • Zeros between other sig figs do. • 1002 • zeroes at the end of a number after the decimal point do count • 45.8300 • If they are holding places, they don’t. • If they are measured (or estimated) they do = 4 sig figs = 6 sig figs

  22. Sig Figs • Only measurements have sig figs. • Counted numbers are exact • A dozen is exactly 12 • A a piece of paper is measured 11 inches tall. • Being able to locate, and count significant figures is an important skill.

  23. Sig figs. • How many sig figs in the following measurements? • 458 g • 4085 g • 4850 g • 0.0485 g • 0.004085 g • 40.004085 g = 3 sig figs = 4 sig figs = 3 sig figs = 3 sig figs = 4 sig figs = 8 sig figs

  24. Sig Figs. • 405.0 g • 4050 g • 0.450 g • 4050.05 g • 0.0500060 g = 4 sig figs = 3 sig figs = 3 sig figs = 6 sig figs = 6 sig figs

  25. Question • 50 is only 1 significant figure • if it really has two, how can I write it? • A zero at the end only counts after the decimal place. • Scientific notation • 5.0 x 101 • now the zero counts. 50.0 = 3 sig figs

  26. Adding and subtracting with sig figs • The last sig fig in a measurement is an estimate. • Your answer when you add or subtract can not be better than your worst estimate. • have to round it to the least place of the measurement in the problem

  27. 27.93 + 6.4 27.93 27.93 + 6.4 6.4 For example • First line up the decimal places Find the estimated numbers in the problem Then do the adding 34.33 This answer must be rounded to the tenths place

  28. Rounding rules • look at the number behind the one you’re rounding. • If it is 0 to 4 don’t change it • If it is 5 to 9 make it one bigger • round 45.462 to four sig figs • to three sig figs • to two sig figs • to one sig fig = 45.46 = 45.5 = 45 = 50

  29. Practice = 11.6756 = 11.7 • 4.8 + 6.8765 • 520 + 94.98 • 0.0045 + 2.113 • 6.0 x 102 - 3.8 x 103 • 5.4 - 3.28 • 6.7 - .542 • 500 -126 • 6.0 x 10-2 - 3.8 x 10-3 = 614.98 = 615 = 2.1175 = 2.118 = 3198 = 3.2 x 103 = 2.12 = 2.1 = 6.158 = 6.2 = 374 = 0.0562 = 5.6 x 10-2

  30. Multiplication and Division • Rule is simpler • Same number of sig figs in the answer as the least in the question • 3.6 x 653 • 2350.8 • 3.6 has 2 s.f. 653 has 3 s.f. • answer can only have 2 s.f. • 2400

  31. Multiplication and Division • practice • 4.5 / 6.245 • 4.5 x 6.245 • 9.8764 x .043 • 3.876 / 1983 • 16547 / 714 = 0.720576 = 0.72 = 28.1025 = 28 = 0.4246852 = 0.42 = 0.001954614 = 0.001955 = 23.17507 = 23.2

  32. The Metric System • Easier to use because it is …… • a decimal system • Every conversion is by some power of …. • 10. • A metric unit has two parts • A prefix and a base unit. • prefix tells you how many times to • divide or multiply by 10.

  33. Base Units • Length - meter more than a yard - m • Mass - grams - a bout a raisin - g • Time - second - s • Temperature - Kelvin or ºCelsius K or C • Energy - Joules- J • Volume - Liter - half f a two liter bottle- L • Amount of substance - mole - mol

  34. Prefixes • Kilo K 1000 times • Hecto H 100 times • Deka D 10 times • deci d 1/10 • centi c 1/100 • milli m 1/1000 • kilometer - about 0.6 miles • centimeter - less than half an inch • millimeter - the width of a paper clip wire

  35. H K D d c m Converting • King Henry Drinks (basically) delicious chocolate milk • how far you have to move on this chart, tells you how far, and which direction to move the decimal place. • The box is the base unit, meters, Liters, grams, etc.

  36. k h D d c m Conversions • Change 5.6 m to millimeters • starts at the base unit and move three to the right. • move the decimal point three to the right 5 6 0 0

  37. k h D d c m Conversions • convert 25 mg to grams • convert 0.45 km to mm • convert 35 mL to liters • It works because the math works, we are dividing or multiplying by 10 the correct number of times (homework) = 0.025 g = 450,000 mm = 0.035 L

  38. Volume • calculated by multiplying L x W x H • Liter the volume of a cube 1 dm (10 cm) on a side • so 1 L = • 10 cm x 10 cm x 10 cm or 1 L = 1000 cm3 • 1/1000 L = • 1 cm3 • Which means 1 mL = 1 cm3

  39. Volume • 1 L about 1/4 of a gallon - a quart • 1 mL is about 20 drops of water or 1 sugar cube

  40. Mass • weight is a • force, • Mass is the • amount of matter. • 1gram is defined as the mass of 1 cm3 of water at 4 ºC. • 1 ml of water = 1 g • 1000 g = • 1000 cm3 of water • 1 kg = 1 L of water

  41. Mass • 1 kg = 2.5 lbs • 1 g = 1 paper clip • 1 mg = 10 grains of salt or 2 drops of water.

  42. Density • how heavy something is for its size • the ratio of mass to volume for a substance • D = M / V M D V

  43. Density is a • Physical Property • The density of an object remains • _________ at _______ ________ • Therefore it is possible to identify an unknown by figuring out its density. • Story & Demo (king and his gold crown) constant constant temperature

  44. What would happen to density if temperature decreased? slow down decrease STAYS THE SAME INCREASE WATER, because it expands. As temperature decreases molecules ______ _____ And come closer together therefore making volume _________ The mass ______ ____ _______ Therefore the density would _______ Exception _____________________ Therefore Density decreases ICE FLOATS

  45. Units for Density • 1. Regularly shaped object in which a ruler is used. ______ • 2. liquid, granular or powdered solid in which a graduated cylinder is used ______ • 3. irregularly shaped object in which the water displacement method must be used _____ g/cm3 g/ml g/ml

  46. Sample Problem: • What is the density of a sample of Copper with a mass of 50.25g and a volume of 6.95cm3? • D = M/V • D = 50.25g / 6.95 cm3 • = 7.2302 = 7.23 cm3

  47. Sample Problem 2. M M = D x V D V M = 0.93 g/ml x 2.4 ml = 2.232 = 2.2 g A piece of wood has a density of 0.93 g/ml and a volume of 2.4 ml What is its mass?

  48. Problem Solving or Dimensional Analysis • Identify the unknown • What is the problem asking for • List what is given and the equalities needed to solve the problem. • Ex. 1 dozen = 12 • Plan a solution • Equations and steps to solve • (conversion factors) • Do the calculations • Check your work: • Estimate; is the answer reasonable • UNITS • All measurements need a NUMBER & A UNIT!!

  49. Dimensional Analysis dimensions • Use the units (__________) to help analyze (______) the problem. • Conversion Factors: Ratios of equal measurements. • Numerator measurement = Denominator measurement • Using conversion factors does not change the value of the measurement • Examples; 1 ft = _____ (_________) 1 ft__ or 12 in (_____________ __________) 12 in 1 ft solve 12 in equality Conversion factors

  50. What you are being asked to solve for in the problem will determine which conversion factors need to be used. 16 5280 365 24 60 60 Common Equalities and their conversion factors: 1 lb = _____oz 1 mi = ______ft 1 yr = ______days 1 day = ____hrs 1 hr = ____min 1 min = ____sec

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