1 Scientific Measurement

2 Measurement in Chemistry In chemistry we  Measure quantities.  Do experiments.  Calculate results.  Use numbers to report measurements.  Compare results to standards.

3 Stating a Measurement In every measurement, a number is followed by a unit. Observe the following examples of measurements: Number and Unit 35 m 0.25 L 225 lb 3.4 hr

4 Qualitative vs. Quantitative Qualitative – descriptive, non-numerical form Quantitative – definite form, usually with numbers and units Fever example

5 Scientific Notation Scientific notation  Is used to write very large or very small numbers.  For the width of a human hair ( m) is written 8 x m  For a large number such as s is written 4.5 x 10 6 s

6 Writing Numbers in Scientific Notation  A number in scientific notation contains a coefficient and a power of 10. coefficient power of ten coefficient power of ten 1.5 x x  To write a number in scientific notation, the decimal point is placed after the first digit.  The spaces moved are shown as a power of ten = 5.2 x = 3.78 x spaces left 3 spaces right

7 Some Powers of Ten TABLE 1.2

8 Comparing Numbers in Standard and Scientific Notation Here are some numbers written in standard format and in scientific notation. Number in Standard Format Scientific Notation Diameter of the Earth m1.28 x 10 7 m Mass of a human 68 kg 6.8 x 10 1 kg Length of a virus cm3 x cm

9 Learning Check Select the correct scientific notation for each. A ) 8 x ) 8 x ) 0.8 x B ) 7.2 x ) 72 x ) 7.2 x 10 -4

10 Solution Select the correct scientific notation for each. A ) 8 x B ) 7.2 x 10 4

11 Learning Check Write each as a standard number. A. 2.0 x ) 2002) ) B. 1.8 x ) ) )

12 Solution Write each as a standard number. A. 2.0 x ) B. 1.8 x )

13 Accuracy, Precision, and Error Accuracy is how close a measurement is to its true value. If weigh yourself and know you weigh 170 lbs, and scale says 20 lbs, not accurate. Precision is how close a series of measurements are to each other.

14 Accuracy and Precision

15 Significant Figures in Measured Numbers Significant figures  Obtained from a measurement include all of the known digits plus the estimated digit.  Reported in a measurement depend on the measuring tool.

16 Error = experimental value – accepted value (can be negative or positive) % error = error / accepted value x 100 Thermometer examples

17 Significant Figures TABLE 1.4

18 All non-zero numbers in a measured number are significant. MeasurementNumber of Significant Figures cm4 5.6 ft lb m5 Counting Significant Figures

19 Sandwiched zeros  Occur between nonzero numbers.  Are significant. MeasurementNumber of Significant Figures 50.8 mm min lb m 5 Sandwiched Zeros

20 Trailing zeros  Follow non-zero numbers in numbers without decimal points.  Are usually place holders.  Are not significant. MeasurementNumber of Significant Figures cm kg mL g 5 Trailing Zeros

21 Leading zeros  Precede non-zero digits in a decimal number.  Are not significant. Measurement Number of Significant Figures mm oz lb mL 3 Leading Zeros

22 Significant Figures in Scientific Notation In scientific notation  All digits including zeros in the coefficient are significant. Scientific NotationNumber of Significant Figures 8 x 10 4 m1 8.0 x 10 4 m x 10 4 m3

23 State the number of significant figures in each of the following measurements: A m B L C g D m Learning Check

24 State the number of significant figures in each of the following measurements: A m2 B L4 C g1 D m3 Solution

25 A. Which answer(s) contains 3 significant figures? 1) ) ) 4.76 x 10 3 B. All the zeros are significant in 1) ) ) x 10 3 C. The number of significant figures in 5.80 x 10 2 is 1) one3) two3) three Learning Check

26 A. Which answer(s) contains 3 significant figures? 2) ) 4.76 x 10 3 B. All the zeros are significant in 2) ) x 10 3 C. The number of significant figures in 5.80 x 10 2 is 3) three Solution

27 In which set(s) do both numbers contain the same number of significant figures? 1) 22.0 and ) and 4.00 x ) and Learning Check

28 Solution In which set(s) do both numbers contain the same number of significant figures? 3) and Both numbers contain two (2) significant figures.

29 Calculations with Measured Numbers In calculations with measured numbers, significant figures or decimal places are counted to determine the number of figures in the final answer.

30 When multiplying or dividing use  The same number of significant figures as the measurement with the fewest significant figures.  Rounding rules to obtain the correct number of significant figures. Example: x = = 5.3 (rounded) 4 SF 2 SF calculator 2 SF Multiplication and Division

31 Give an answer for the following with the correct number of significant figures: A x 4.2 = 1) 9 2) 9.2 3) B ÷ 0.07 = 1) ) 62 3) 60 C x = x ) 11.32) 11 3) Learning Check

32 A x 4.2 = 2) 9.2 B ÷ 0.07 = 3) 60 C x = 2) x On a calculator, enter each number followed by the operation key x   = = 11 (rounded) Solution

33 When adding or subtracting use  The same number of decimal places as the measurement with the fewest decimal places.  Rounding rules to adjust the number of digits in the answer one decimal place two decimal places 26.54calculated answer 26.5 answer with one decimal place Addition and Subtraction

34 For each calculation, round the answer to give the correct number of significant figures. A = 1) 257 2) ) B = 1) ) ) 40.7 Learning Check

35 A rounds to 257 Answer (1) B round to 40.7Answer (3) Solution

36 The Metric System (SI) The metric system or SI (international system) is  A decimal system based on 10.  Used in most of the world.  Used everywhere by scientists.

37 Units in the Metric System In the metric and SI systems, one unit is used for each type of measurement: MeasurementMetricSI Lengthmeter (m)meter (m) Volumeliter (L)cubic meter (m 3 ) Massgram (g)kilogram (kg) Timesecond (s)second (s) TemperatureCelsius (  C)Kelvin (K)

38 For each of the following, indicate whether the unit describes 1) length 2) mass or 3) volume. ____ A. A bag of tomatoes is 4.6 kg. ____ B. A person is 2.0 m tall. ____ C. A medication contains 0.50 g aspirin. ____ D. A bottle contains 1.5 L of water. Learning Check

39 For each of the following, indicate whether the unit describes 1) length 2) mass or 3) volume. 2 A. A bag of tomatoes is 4.6 kg. 1 B. A person is 2.0 m tall. 2 C. A medication contains 0.50 g aspirin. 3 D. A bottle contains 1.5 L of water. Solution

40 Learning Check Identify the measurement that has a SI unit. A. John’s height is 1) 1.5 yd2) 6 ft 3) 2.1 m B. The race was won in 1) 19.6 s2) 14.2 min3) 3.5 hr C. The mass of a lemon is 1) 12 oz2) kg3) 0.6 lb D. The temperature is 1) 85  C2) 255 K3) 45  F

41 Solution A. John’s height is 3) 2.1 m B. The race was won in 1) 19.6 s C. The mass of a lemon is 2) kg D. The temperature is 2) 255 K

42 Prefixes A prefix  In front of a unit increases or decreases the size of that unit.  Make units larger or smaller than the initial unit by one or more factors of 10.  Indicates a numerical value. prefixvalue 1 kilometer=1000 meters 1 kilogram=1000 grams

43 Metric and SI Prefixes TABLE 1.6 Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cmings

44 Indicate the unit that matches the description: 1. A mass that is 1000 times greater than 1 gram. 1) kilogram2) milligram3) megagram 2. A length that is 1/100 of 1 meter. 1) decimeter2) centimeter3) millimeter 3. A unit of time that is 1/1000 of a second. 1) nanosecond 2) microsecond 3) millisecond Learning Check

45 Indicate the unit that matches the description: 1. A mass that is 1000 times greater than 1 gram. 1) kilogram 2. A length that is 1/100 of 1 meter. 2) centimeter 3. A unit of time that is 1/1000 of a second. 3) millisecond Solution

46 Select the unit you would use to measure A. Your height 1) millimeters2) meters 3) kilometers B. Your mass 1) milligrams2) grams 3) kilograms C. The distance between two cities 1) millimeters2) meters 3) kilometers D. The width of an artery 1) millimeters2) meters 3) kilometers Learning Check

47 A. Your height 2) meters B. Your mass 3) kilograms C. The distance between two cities 3) kilometers D. The width of an artery 1) millimeters Solution

48 An equality  States the same measurement in two different units.  Can be written using the relationships between two metric units. Example: 1 meter is the same as 100 cm and 1000 mm. 1 m=100 cm 1 m=1000 mm Metric Equalities

49 Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings Measuring Length

50 Measuring Volume Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

51 Measuring Mass  Several equalities can be written for mass in the metric (SI) system 1 kg =1000 g 1 g =1000 mg 1 mg = g 1 mg =1000 µg Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cmings

52 Indicate the unit that completes each of the following equalities: A m = 1) 1 mm 2) 1 km3) 1dm B g = 1) 1 mg2) 1 kg3) 1dg C. 0.1 s = 1) 1 ms2) 1 cs3) 1ds D m = 1) 1 mm 2) 1 cm3) 1dm Learning Check

53 Indicate the unit that completes each of the following equalities: A. 2) 1000 m = 1 km B. 1) g = 1 mg C. 3) 0.1 s = 1 ds D. 2) 0.01 m = 1 cm Solution

54 Complete each of the following equalities: A. 1 kg = 1) 10 g2) 100 g 3) 1000 g B. 1 mm =1) m2) 0.01 m 3) 0.1 m Learning Check

55 Complete each of the following equalities: A. 1 kg = 1000 g (3) B. 1 mm = m (1) Solution

56 Writing Conversion Factors

57 Equalities  Use two different units to describe the same measured amount.  Are written for relationships between units of the metric system, U.S. units, or between metric and U.S. units. For example, 1 m = 1000 mm 1 lb = 16 oz 2.20 lb = 1 kg Equalities

58 Some Common Equalities TABLE 1.9

59 Equalities on Food Labels The contents of packaged foods  In the U.S. are listed as both metric and U.S. units.  Indicate the same amount of a substance in two different units.

60 A conversion factor  Is a fraction obtained from an equality. Equality: 1 in. = 2.54 cm  Is written as a ratio with a numerator and denominator.  Can be inverted to give two conversion factors for every equality. 1 in. and 2.54 cm 2.54 cm 1 in. Conversion Factors

61 Write conversion factors for each pair of units: A. liters and mL B. hours and minutes C. meters and kilometers Learning Check

62 Write conversion factors for each pair of units: A. liters and mL Equality: 1 L = 1000 mL 1 L and 1000 mL 1000 mL 1 L B. hours and minutes Equality: 1 hr = 60 min 1 hr and 60 min 60 min 1 hr C. meters and kilometers Equality: 1 km = 1000 m 1 km and 1000 m 1000 m 1 km Solution

63 A conversion factor  May be obtained from information in a word problem.  Is written for that problem only. Example 1: The price of one pound (1 lb) of red peppers is $ lb red peppers and$2.39 $2.391 lb red peppers Example 2: The cost of one gallon (1 gal) of gas is $ gallon of gasand $2.94 $2.941 gallon of gas Conversion Factors in a Problem

64 A percent factor  Gives the ratio of the parts to the whole. % =Parts x 100 Whole  Use the same units for the parts and whole.  Uses the value 100 and a unit for the whole.  Can be written as two factors. Example: A food contains 30% (by mass) fat. 30 g fat and100 g food 100 g food30 g fat Percent as a Conversion Factor

65 Learning Check Write the equality and conversion factors for each of the following: A. meters and centimeters B. jewelry that contains 18% gold C. one gallon of gas is $ 2.95

66 Solution A meters and centimeters 1m and 100 cm 100 cm 1m B. jewelry that contains 18% gold 18 g gold and 100 g jewelry 100 g jewelry 18 g gold C. one gallon of gas is $ gal and $2.95 $ gal

67 Density

68 Problem Solving

69 To solve a problem  Identify the initial unit.  Identify the final unit. Problem: A person has a height of 2.0 meters. What is that height in inches? The initial unit is the given unit of height. initial unit = meters (m) The final unit is the unit for the answer. final unit = inches (in.) Initial and Final Units

70 Learning Check An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? Identify the initial and final units given in this problem. Initial unit= _______ Final unit = _______

71 Solution An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? Identify the initial and final units given in this problem. Initial unit=pints Final unit =milliliters

72  Write the initial and final units.  Write a unit plan to convert the initial unit to the final unit.  Write equalities and conversion factors.  Use conversion factors to cancel the initial unit and provide the final unit. Unit 1 x Unit 2 = Unit 2 Unit 1 Initial x Conversion= Final unit factor unit Problem Setup

73 Guide to Problem Solving The steps in the Guide to Problem Solving are useful in setting up a problem with conversion factors.

74 Setting up a Problem How many minutes are 2.5 hours? Initial unit= 2.5 hr Final unit=? min Plan=hr min Setup problem to cancel hours (hr). Initial Conversion Final unit factor unit 2.5 hr x 60 min = 150 min (2 SF) 1 hr

75 A rattlesnake is 2.44 m long. How many centimeters long is the snake? 1) 2440 cm 2)244 cm 3)24.4 cm Learning Check

76 A rattlesnake is 2.44 m long. How many centimeters long is the snake? 2) 244 cm 2.44 m x 100 cm = 244 cm 1 m Solution

77  Often, two or more conversion factors are required to obtain the unit needed for the answer. Unit 1 Unit 2Unit 3  Additional conversion factors are placed in the setup to cancel each preceding unit Initial unit x factor 1 x factor 2 = Final unit Unit 1 x Unit 2 x Unit 3 = Unit 3 Unit 1 Unit 2 Using Two or More Factors

78 How many minutes are in 1.4 days? Initial unit: 1.4 days Factor 1 Factor 2 Plan: days hr min Set up problem: 1.4 days x 24 hr x 60 min = 2.0 x 10 3 min 1 day 1 hr 2 SF Exact Exact = 2 SF Example: Problem Solving

79  Be sure to check your unit cancellation in the setup.  The units in the conversion factors must cancel to give the correct unit for the answer. What is wrong with the following setup? 1.4 day x 1 day x 1 hr 24 hr 60 min Units = day 2 /min is not the unit needed Units don’t cancel properly. Check the Unit Cancellation

80 Guide to Problem Solving What is 165 lb in kg? STEP 1 Initial 165 lb Final: kg STEP 2 Plan lb kg STEP 3 Equalities/Factors 1 kg = 2.20 lb 2.20 lb and 1 kg 1 kg 2.20 lb STEP 4 Set Up Problem 165 lb x 1 kg = 74.8 kg 2.20 lb

81 A bucket contains 4.65 L of water. How many gallons of water is that? Unit plan: L qt gallon Equalities:1.06 qt = 1 L 1 gal = 4 qt Learning Check

82 Initial : 4.65 L Final: gallons Plan: L qt gallon Equalities: 1.06 qt = 1 L; 1 gal = 4 qt Set Up Problem: 4.65 L x x 1.06 qt x 1 gal = 1.23 gal 1 L 4 qt 3 SF 3 SF exact 3 SF Solution

83 If a ski pole is 3.0 feet in length, how long is the ski pole in mm? (2.54 cm = 1 inch) Learning Check

ft x 12 in x 2.54 cm x 10 mm = 1 ft 1 in. 1 cm Calculator answer: mm Final answer:910 mm (2 SF rounded) Check factor setup: Units cancel properly Check final unit: mm Solution 3.0 ft x 12 in x 2.54 cm x 10 mm = 1 ft 1 in. 1 cm Calculator answer: mm Final answer:910 mm (2 SF rounded)

85 If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7500 feet? (1 inch = 2.54 cm) Learning Check

86 Initial: 7500 ft65 m/minFinal: min Plan: ft in. cm m min Equalities: 1 ft = 12 in. 1 in. = 2.54 cm 1 m = 100 cm 1 min = 65 m (walking pace) Set Up Problem 7500 ft x 12 in. x 2.54 cm x 1m x 1 min 1 ft 1 in. 100 cm 65 m = 35 min final answer (2 SF) Solution

87 Percent Factor in a Problem If the thickness of the skin fold at the waist indicates an 11% body fat, how much fat is in a person with a mass of 86 kg? percent factor 86 kg x 11 kg fat 100 kg = 9.5 kg fat

88 How many lb of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? Learning Check

89 How many lb of sugar are in 120 g of candy if the candy is 25%(by mass) sugar? % factor 120 g candy x 1 lb candy x 25 lb sugar 454 g candy 100 lb candy = lb sugar Solution