1 Scientific measurement

2 Types of observations l Qualitative- descriptive, but not true measurements –Hot –Large l Quantitative- describe with numbers and units –100  C –15 meters

3 Types of observations l Scientists prefer l Quantitative –More precise –No bias –testable

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

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

6 Let’s use a golf analogy

7 Accurate?No Precise?Yes

8 Accurate?Yes Precise?Yes

9 Precise?No Accurate?Maybe?

10 Accurate?Yes Precise?We cant say!

11 In terms of measurement l Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. l Were they precise? l Were they accurate?

12 Error l Accepted value – The right answer –Based on reliable references l Experimental Value- what you get in lab l Error = experimental value – accepted value l Can be negative

13 Percent Error l Absolute value of error l I know that I weigh 150 kg. If I weigh myself and the balance says 165 kg, what is the percent error?

14 Significant figures (sig figs) l How many numbers mean anything. l When we measure something, we can (and do) always estimate between the smallest marks

15 Significant figures (sig figs) l The better marks the better we can estimate. l Scientist always understand that the last number measured is actually an estimate

16 Significant figures (sig figs) l The measurements we write down tell us about the ruler we measure with l The last digit is between the lines l What is the smallest mark on the ruler that measures cm?

17 Significant figures (sig figs) l What is the smallest mark on the ruler that measures 142 cm?

18 l 140 cm? l Here there’s a problem is the zero significant or not?

19 l 140 cm? l They needed a set of rules to decide which zeroes count. l All other numbers do count

20 Which zeros don’t count as sig figs? l Those at the end of a number before the decimal point don’t count. l l If the number is smaller than one, zeroes before the first number don’t count. l l These zeros are only place holders

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

23 Problem l 50 is only 1 significant figure. l if it really has two, how can I write it? l A zero at the end only counts after the decimal place. l Scientific notation. l 5.0 x 10 1 l now the zero counts.

24 l 1.40 x 10 2 cm l 140 cm

25 Sig figs. l How many sig figs in the following measurements? l 458 g l 4085 g l 4850 g l g l g l g l g l 4050 g l g l g l g

26 Rounding rules l Look at the number behind the one you’re rounding. l If it is 0 to 4 don’t change it. l If it is 5 to 9 make it one bigger. l Round to four sig figs. l to three sig figs. l to two sig figs. l to one sig figs

27 Numbers without sig figs l Counted numbers –12 eggs in a dozen –32 students in a class l Definitions –1 m = 100 cm –16 ounces is 1 pound l No estimated numbers l Unlimited significant figures

28 Scientific notation l All non-zero digits in scientific notation are significant figures. l Any ending zero will be after the decimal point to be significant l 1.20 x 10 3 l Sometimes you must write in scientific notation to use the correct sig figs.

29 Watch the Sig Figs l When rounding, you don’t change the size of the number. l You should end up with a number about the same size. l Use place holders- they’re not significant. –Round to 3 sig figs –Round to 3 sig figs

30 Pacific Atlantic PresentAbsent If the decimal point is absent, start at the Atlantic (right), find the first non zero, and count all the rest of the digits

31 Pacific Atlantic PresentAbsent If the decimal point is PRESENT, start at the Pacific (left), find the first non zero, and count all the rest of the digits

32 Using your calculator with scientific notation l EE and EXP button stand for x 10 to the l 4.5 x l push 4.5 l push either EXP or EE l push 4 +/- or -4 l see what your display says.

33 Practice these problems u (4.8 x 10 5 ) x (6.7 x ) u (6.8 x ) (3.2 x 10 4 ) l Remember when you multiply you add exponents l 10 6 x l When you divide you subtract exponents.

34 Adding and Subtracting l You can’t add or subtract numbers until they are to the same power of ten. l Your calculator does this automatically. l (4.8 x 10 5 ) + (6.7 x 10 6 ) l (6.8 x ) -(3.2 x ) l Remember- standard form starts with a number between 1 and 10 to start.

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

36 For example l First line up the decimal places Then do the adding Find the estimated numbers in the problem This answer must be rounded to the tenths place.

37 Practice l l l l l 6.0 x x 10 2 l 6.0 x x l 5.33 x x 10 21

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

39 Multiplication and Division l Same rules for division. l practice l 4.5 / l 4.5 x l x.043 l / 1980 l / 710

40 The Metric System

41 Measuring l The numbers are only half of a measurement. l It is 10 long. l 10 what? l Numbers without units are meaningless. l How many feet in a yard? l A mile? l A rod?

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

43 Base Units l Length - meter - more than a yard - m l Mass - grams - about a raisin - g l Time - second - s l Temperature - Kelvin or ºCelsius K or ºC l Energy - Joules- J l Volume - Liter - half of a two liter bottle- L l Amount of substance - mole - mol

44 Prefixes l kilo k 1000 times l deci d 1/10 l centi c 1/100 l milli m 1/1000 l micro μ 1/ l nano n 1/ l kilometer - about 0.6 miles l centimeter - less than half an inch l millimeter - the width of a paper clip wire

45 Volume l calculated by multiplying L x W x H l Liter the volume of a cube 1 dm (10 cm) on a side l 1L = 1 dm 3 l so 1 L = 10 cm x 10 cm x 10 cm l 1 L = 1000 cm 3 l 1/1000 L = 1 cm 3 l 1 mL = 1 cm 3

46 Volume l 1 L about 1/4 of a gallon - a quart l 1 mL is about 20 drops of water or 1 sugar cube

47 Mass l 1 gram is defined as the mass of 1 cm 3 of water at 4 ºC. l 1000 g = 1000 cm 3 of water l 1 kg = 1 L of water

48 Mass l 1 kg = 2.5 lbs l 1 g = 1 paper clip l 1 mg = 10 grains of salt

49 Converting khDdcm l how far you have to move on this chart, tells you how far, and which direction to move the decimal place. l The box is the base unit, meters, Liters, grams, etc.

50 Conversions l Change 5.6 m to millimeters khDdcm l starts at the base unit and move three to the right. l move the decimal point three to the right 5600

51 Conversions l convert 25 mg to grams l convert 0.45 km to mm l convert 35 mL to liters l It works because the math works, we are dividing or multiplying by 10 the correct number of times. khDdcm

52 What about micro- and nano-? l The jump in between is 3 places l Convert μm to m l Convert cm to nm khDdcmμn 33

53 Measuring Temperature l Celsius scale. l water freezes at 0ºC l water boils at 100ºC l body temperature 37ºC l room temperature ºC 0ºC

54 Measuring Temperature l Kelvin starts at absolute zero (-273 º C) l degrees are the same size l C = K -273 l K = C l Kelvin is always bigger. l Kelvin can never be negative. 273 K

55 Temperature is different l from heat. l Temperature is which way heat will flow. (from hot to cold) l Heat is energy, ability to do work. l A drop of boiling water hurts, l kilogram of boiling water kills.

56 Units of energy are l calories or Joules l 1 calorie is the amount of heat needed to raise the temperature of 1 gram of water by 1ºC. l A food Calorie is really a kilocalorie. l 1 calorie = 4.18 J

57 Conversion factors l “A ratio of equivalent measurements.” l Start with two things that are the same. 1 m = 100 cm l Can divide by each side to come up with two ways of writing the number 1.

58 Conversion factors 100 cm1 m= 100 cm

59 Conversion factors 1 1 m= 100 cm

60 Conversion factors 1 1 m= 100 cm =1 m

61 Conversion factors 1 1 m= 100 cm = 1 m 1

62 Conversion factors l A unique way of writing the number 1. l In the same system they are defined quantities so they have unlimited significant figures. l Equivalence statements always have this relationship. l big # small unit = small # big unit l 1000 mm = 1 m

63 Write the conversion factors for the following l kilograms to grams l feet to inches l qt. = 1.00 L

64 What are they good for? n We can multiply by one creatively to change the units. n 13 inches is how many yards? n 36 inches = 1 yard. n 1 yard = 1 36 inches n 13 inches x 1 yard = 36 inches

65 Conversion factors l Called conversion factors because they allow us to convert units. l Really just multiplying by one, in a creative way. l Choose the conversion factor that gets rid of the unit you don’t want.

66 Dimensional Analysis l Dimension = unit l Analyze = solve l Using the units to solve the problems. l If the units of your answer are right, chances are you did the math right.

67 Dimensional Analysis l Using with metric units l Need to know equivalence statements l If it has a prefix, get rid of it with one conversion factor l To add a prefix use a conversion factor

68 Practice l 25 mL is how many L? l 5.8 x mm is how many nm?

69 Dimensional Analysis l In the same system, unlimited sig figs l From one system to another. The conversion factor has as many the most sig figs in the measurements. l 1 inch is 2.54 cm l 3 sf 1 inch 2.54 cm

70 Dimensional Analysis l A race is 10.0 km long. How far is this in miles? – 1 mile = 1760 yds – 1 meter = yds

71 Dimensional Analysis l Pikes peak is 14,110 ft above sea level. What is this in meters? – 1 mile = 1760 yds – 1 meter = yds

72 Dimensional Analysis l Another measuring system has different units of measure. 6 ft = 1 fathom 100 fathoms = 1 cable length 10 cable lengths = 1 nautical mile 3 nautical miles = 1 league l Jules Verne wrote a book 20,000 leagues under the sea. How far is this in feet?

73 Multiple units l The speed limit is 65 mi/hr. What is this in m/s? –1 mile = 1760 yds – 1 meter = yds 65 mi hr 1760 yd 1 mi1.094 yd 1 m1 hr 60 min 1 min 60 s

74 Multiple units l Lead has a density of 11.4 g/mL. What is this in pounds per quart? –454 g = 1 lb –1 L = 1.06 qt

75 Units to a Power l How many m 3 is 1500 cm 3 ? cm 3 1 m 100 cm 1 m 100 cm 1 m 100 cm cm 3 1 m 100 cm 3

76 Units to a Power l How many cm 2 is 15 m 2 ? l 36 cm 3 is how many mm 3 ?

77 l A European cheese making recipe calls for 2.50 kg of whole milk. An American wishes to make the recipe has only measuring cups, which are marked in cups. If the density of milk is 1.03 g/cm 3 how many cups of milk does he need? 1 qt = 2 pints 1 yd = 3 ft. 1 mile = 1.61 km 1 m = yds 1 L = 1000 cm 3 1 gal = 4 qt 1 L = 1.06 qt 1 lb = 454 g 1 mi =1760 yds 1 pint = 2 cups

78 l A barrel of petroleum holds 42.0 gal. Empty it weighs 75 lbs. When it is filled with ethanol it weighs 373 lbs. What is the density of ethanol in g/cm 3 ? 1 qt = 2 pints 1 yd = 3 ft. 1 mile = 1.61 km 1 m = yds 1 L = 1000 cm 3 1 gal = 4 qt 1 L = 1.06 qt 1 lb = 454 g 1 mi =1760 yds 1 pint = 2 cups

79 Which is heavier? it depends

80 Density l How heavy something is for its size. l The ratio of mass to volume for a substance. l D = M / V l Independent of how much of it you have l gold - high density l air low density. l Table 3.6 pg 90

81

82 Calculating l The formula tells you how. l Units will be g/mL or g/cm 3 l A piece of wood has a mass of 11.2 g and a volume of 23 mL what is the density? l A piece of wood has a density of 0.93 g/mL and a volume of 23 mL what is the mass?

83 Calculating l A piece of wood has a density of 0.93 g/mL and a mass of 23 g what is the volume? l The units must always work out. l Algebra 1 l Get the thing you want on the top, l Then get it by itself. l What ever you do to one side, do to the other.

84 Floating l Lower density floats on higher density. l Ice is less dense than water. l Most wood is less dense than water. l Helium is less dense than air. l A ship is less dense than water.

85 Density of water l 1 g of water is 1 mL of water. l density of water is 1 g/mL l at 4ºC l otherwise it is less

86 Density as a conversion factor l Aluminum has a density of 2.70 g/cm 3 l That means 2.70 g of aluminum is 1 cm 3 l Can make conversion factors l What is the mass of 25 cm 3 of aluminum? g cm 3 25 cm = 68 g

87 Density as a conversion factor l Aluminum has a density of 2.70 g/cm 3 l What is the volume of 350 g of aluminum? cm 3 g 350 g = 130 cm 3

How to measure Mass

How to Measure Volume Graduated Cylinder Come in variety of sizes measure milliliters

l Meniscus - the curve the water takes in the cylinder How to Measure Volume l Meaure at the bottom of the meniscus.