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EQ: What is the difference between qualitative and quantitative observations? Section 1 Scientific Method Chapter 2

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Class Starter 9/9: Check the EQ and Memory Verse. Write down what you need to. Today’s Section Title is “2.1 Scientific Method” Pick up a green Problem-Solving Workbook from the crate under the TV. Read through pages 1 and 2 to review and complete #1, a-e on page 11 in your Cornell Notes. Show your work. Section 1 Scientific Method Chapter 2

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Scientific Method a logical approach to solving problems by: observing and collecting data formulating hypotheses testing hypotheses formulating theories that are supported by data. Section 1 Scientific Method Chapter 2

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Observing and Collecting Data Observing - using the senses to obtain information. information may be qualitative (descriptive) quantitative (numerical) System: isolated matter in a given area that is studied during an experiment or observation. Scientists use data to make generalizations, which they use to formulate a hypothesis, or testable statement Section 1 Scientific Method Chapter 2

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Testing Hypotheses Experiments provide data to support or refute a hypothesis or theory. Controls are the experimental conditions that remain constant. Variables are any experimental conditions that change. Section 1 Scientific Method Chapter 2

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Theorizing A model explains how phenomena occur and how data or events are related. visual, verbal, or mathematical example: atomic model of matter A theory is a broad generalization that explains a body of facts or phenomena. example: atomic theory Section 1 Scientific Method Chapter 2

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Scientific Method Section 1 Scientific Method Chapter 2

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EQ: Section 2 Units of Measurement Chapter 2 What are the SI base units?

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Class Starter Would you be breaking the speed limit in a 40 mi/h zone if you were traveling at 60 km/h? ( one kilometer = 0.62 miles ) Section 2 Units of Measurement Chapter 2

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Units of Measurement Measurements represent quantities. A quantity is something that has magnitude, size, or amount. The choice of unit depends on the quantity being measured. Section 2 Units of Measurement Chapter 2

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SI Measurement Scientists all over the world have agreed on a single measurement system called Le Système International d’Unités, abbreviated SI. Section 2 Units of Measurement Chapter 2 SI has seven base units

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SI Base Units Section 2 Units of Measurement Chapter 2

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SI Base Units Mass Mass is a measure of the quantity of matter. The SI standard unit for mass is the kilogram. Weight is a measure of the gravitational pull on matter. Mass does not depend on gravity. Section 2 Units of Measurement Chapter 2

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SI Base Units Length Length is a measure of distance. The SI standard for length is the meter. Section 2 Units of Measurement Chapter 2

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Derived SI Units Combinations of SI base units form derived units. pressure is measured in kg/ms 2, or pascals Section 2 Units of Measurement Chapter 2

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Derived SI Units, continued Volume Volume is the amount of space occupied by an object. The derived SI unit is cubic meters, m 3 The cubic centimeter, cm 3 or cc, is often used The liter, L, is a non-SI unit 1 L = 1000 cm 3 1 mL = 1 cm 3 Section 2 Units of Measurement Chapter 2

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Derived SI Units, continued Density Density is the ratio of mass to volume, or mass divided by volume. Section 2 Units of Measurement Chapter 2 The derived SI unit is kilograms per cubic meter, kg/m 3 g/cm 3 or g/mL are also used Density is a characteristic physical property of a substance.

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Derived SI Units, continued Density Density can be used as one property to help identify a substance Section 2 Units of Measurement Chapter 2

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Click below to watch the Visual Concept. Visual Concept Chapter 2 Section 2 Units of Measurement Equation for Density

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Sample Problem A A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm 3. Calculate the density of aluminum. Section 2 Units of Measurement Chapter 2 Derived SI Units, continued

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Sample Problem A Solution Given: mass (m) = 8.4 g volume (V) = 3.1 cm 3 Unknown: density (D) Solution: Section 2 Units of Measurement Chapter 2

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Class Starter 9/11. Check EQ and MV. A sample of metal has a mass of 12.0 g. The volume of the sample is 4.0 cm 3. Calculate the density of the metal.

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Conversion Factors A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other. example: How quarters and dollars are related Section 2 Units of Measurement Chapter 2

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Click below to watch the Visual Concept. Visual Concept Chapter 2 Section 2 Units of Measurement Conversion Factor

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Conversion Factors, continued Dimensional analysis is a mathematical technique that allows you to use units to solve problems involving measurements. Section 2 Units of Measurement Chapter 2 quantity sought = quantity given × conversion factor example: the number of quarters in 12 dollars number of quarters = 12 dollars × conversion factor

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Using Conversion Factors Section 2 Units of Measurement Chapter 2

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example: conversion factors for meters and decimeters Conversion Factors, continued Deriving Conversion Factors You can derive conversion factors if you know the relationship between the unit you have and the unit you want. Section 2 Units of Measurement Chapter 2

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SI Conversions Section 2 Units of Measurement Chapter 2

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Conversion Factors, continued Sample Problem B Express a mass of 5.712 grams in milligrams and in kilograms. Section 2 Units of Measurement Chapter 2

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Conversion Factors, continued Sample Problem B Solution Express a mass of 5.712 grams in milligrams and in kilograms. Given: 5.712 g Unknown: mass in mg and kg Solution: mg 1 g = 1000 mg Possible conversion factors: Section 2 Units of Measurement Chapter 2

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Sample Problem B Solution, continued Express a mass of 5.712 grams in milligrams and in kilograms. Given: 5.712 g Unknown: mass in mg and kg Solution: kg 1 000 g = 1 kg Possible conversion factors: Conversion Factors, continued Section 2 Units of Measurement Chapter 2

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Class Starter 9/13. Check EQ and MV. Section 3 Using Scientific Measurements Chapter 2 Turn in your Density Worksheet from yesterday, if you haven’t already. 1.Express a mass of 12.34 grams in milligrams and in kilograms. 2.Calculate the density of a substance of a material whose mass is 5.6 g and has a volume of 10.3 mL.

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Objectives Distinguish between accuracy and precision. Determine the number of significant figures in measurements. Perform mathematical operations involving significant figures. Convert measurements into scientific notation. Distinguish between inversely and directly proportional relationships. Section 3 Using Scientific Measurements Chapter 2

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Accuracy and Precision Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. Precision refers to the closeness of a set of measurements of the same quantity made in the same way. Section 3 Using Scientific Measurements Chapter 2

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Accuracy and Precision Section 3 Using Scientific Measurements Chapter 2

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Accuracy and Precision, continued Percentage Error Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100. Section 3 Using Scientific Measurements Chapter 2

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Accuracy and Precision, continued Sample Problem C A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percentage error of the student’s measurement? Section 3 Using Scientific Measurements Chapter 2

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Accuracy and Precision, continued Sample Problem C Solution Section 3 Using Scientific Measurements Chapter 2

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Accuracy and Precision, continued Error in Measurement Some error or uncertainty always exists in any measurement. skill of the measurer conditions of measurement measuring instruments Section 3 Using Scientific Measurements Chapter 2

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Significant Figures Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. The term significant does not mean certain. Section 3 Using Scientific Measurements Chapter 2

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Reporting Measurements Using Significant Figures Section 3 Using Scientific Measurements Chapter 2

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Significant Figures, continued Determining the Number of Significant Figures Section 3 Using Scientific Measurements Chapter 2

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Click below to watch the Visual Concept. Visual Concept Chapter 2 Section 3 Using Scientific Measurements Significant Figures

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Click below to watch the Visual Concept. Visual Concept Chapter 2 Section 3 Using Scientific Measurements Rules for Determining Significant Zeros

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Significant Figures, continued Sample Problem D How many significant figures are in each of the following measurements? a. 28.6 g b. 3440. cm c. 910 m d. 0.046 04 L e. 0.006 700 0 kg Section 3 Using Scientific Measurements Chapter 2

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Sample Problem D Solution a.28.6 g There are no zeros, so all three digits are significant. b. 3440. cm By rule 4, the zero is significant because it is immediately followed by a decimal point; there are 4 significant figures. c. 910 m By rule 4, the zero is not significant; there are 2 significant figures. Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued

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Sample Problem D Solution, continued d. 0.046 04 L By rule 2, the first two zeros are not significant; by rule 1, the third zero is significant; there are 4 significant figures. e. 0.006 700 0 kg By rule 2, the first three zeros are not significant; by rule 3, the last three zeros are significant; there are 5 significant figures. Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued

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Class Starter 9/16. Check EQ and MV. How many significant figures are in each of the following measurements? a. 28.60 kg b. 34640 m c. 70. L d. 0.00591040 cm e. 0.009400 g Section 3 Using Scientific Measurements Chapter 2

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Significant Figures, continued Addition or Subtraction with Significant Figures When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. Multiplication or Division with Significant Figures For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest total number of significant figures. Section 3 Using Scientific Measurements Chapter 2

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Significant Figures, continued Rounding Section 3 Using Scientific Measurements Chapter 2

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Sample Problem E Carry out the following calculations. Express each answer to the correct number of significant figures. a. 5.44 m - 2.6103 m b. 2.4 g/mL 15.82 mL Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued

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Sample Problem E Solution a.5.44 m - 2.6103 m = 2.84 m Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued There should be two digits to the right of the decimal point, to match 5.44 m. b. 2.4 g/mL 15.82 mL = 38 g There should be two significant figures in the answer, to match 2.4 g/mL.

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Significant Figures, continued Conversion Factors and Significant Figures There is no uncertainty exact conversion factors. Most exact conversion factors are defined quantities. Section 3 Using Scientific Measurements Chapter 2

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Significant Figures, class work Pick up a worksheet. Section 3 Using Scientific Measurements Chapter 2

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Class Starter 9/17. Check EQ and MV. Check your answers from the Sig Fig worksheet I.Counting 1.4 2.5 3.3 4.4 5.3 6.4 7.5 8.3 9.3 10.3 11.2 12.5 13.3 14.3 15.7 16.5 17.4 18.4 19.3 20.4 Section 3 Using Scientific Measurements Chapter 2

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Class Starter 9/17. Check EQ and MV. Check your answers from the Sig Fig worksheet II.Add 1.20. cm 2.0.29 cm 3.14.383 g 4.173.6 g 5.506.7 cm 6.246.62 cm 7.0.2704 g 8.3.89 x 10 -4 cm 9.270.6 mL 10.10.8 x 10 2 g III.Subtract 1.17.74 cm 2.245 g 3.116.7 mL 4.22.6 g 5.10.914 mL Section 3 Using Scientific Measurements Chapter 2

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Class Starter 9/17. Check EQ and MV. Check your answers from the Sig Fig worksheet II.Mulitply 1.11.6 cm 2 2.110 cm 2 3.3.7 m 2 4.36.6 mm 2 5.2560 dm 2 6.20 cm 2 7.20 cm 2 8.25 cm 2 9.10 x 10 5 m 2 10.11 x 10 -7 cm 2 11.27 cm 2 12.600 m 2 13.850 km 2 14.46 x 10 -14 m 2 15.4.21 x 10 7 m 2 III.Divide 1.1.914 cm 2.18.82 m 3.570 km 4.7.1 mm 5.0.4891 cm Section 3 Using Scientific Measurements Chapter 2

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In scientific notation, numbers are written in the form M × 10 n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number. example: 0.000 12 mm = 1.2 × 10 −4 mm Scientific Notation Section 3 Using Scientific Measurements Chapter 2 Move the decimal point four places to the right and multiply the number by 10 −4.

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Scientific Notation, continued M x 10 n 1. Determine M by moving the decimal point in the original number to the left or the right so that only one nonzero digit remains to the left of the decimal point. 2. Determine n by counting the number of places that you moved the decimal point. If you moved it to the left, n is positive. If you moved it to the right, n is negative. Section 3 Using Scientific Measurements Chapter 2

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Scientific Notation, continued Mathematical Operations Using Scientific Notation 1. Addition and subtraction —These operations can be performed only if the values have the same exponent (n factor). example: 4.2 × 10 4 kg + 7.9 × 10 3 kg or Section 3 Using Scientific Measurements Chapter 2

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2. Multiplication —The M factors are multiplied, and the exponents are added algebraically. example: (5.23 × 10 6 µm)(7.1 × 10 −2 µm) = (5.23 × 7.1)(10 6 × 10 −2 ) = 37.133 × 10 4 µm 2 = 3.7 × 10 5 µm 2 Section 3 Using Scientific Measurements Chapter 2 Scientific Notation, continued Mathematical Operations Using Scientific Notation

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3. Division — The M factors are divided, and the exponent of the denominator is subtracted from that of the numerator. example: Section 3 Using Scientific Measurements Chapter 2 Scientific Notation, continued Mathematical Operations Using Scientific Notation = 0.6716049383 × 10 3 = 6.7 10 2 g/mol

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Click below to watch the Visual Concept. Visual Concept Chapter 2 Section 3 Using Scientific Measurements Scientific Notation

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Class Starter 9/18. Check EQ and MV. Check your answers from the Sig Fig worksheet I.Convert a)3.427 x 10 -3 b)4.56 x 10 -3 c)1.23453 x 10 5 d)1.72 x 10 2 e)9.84 x 10 -4 f)5.02 x 10 -1 g)3.1000 x 10 5 h)1.14 x 10 2 i)1.072 x 10 2 j)4.55 x 10 -5 k)2.2052 x 10 3 l)3.00 x 10 -1 m)9.82 x 10 -4 n)4.73 x 10 -2 o)6.50502x10 2 p)3.03 x 10 -1 q)2.04 x 10 6 r)1.29 x 10 0 s)5.65 x 10 -3 t)1.3622052 x 10 6 u)4.500 x 10 5 v)1.000 x 10 0 Section 3 Using Scientific Measurements Chapter 2

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Class Starter 9/18. Check EQ and MV. Check your answers from the Sig Fig worksheet 3.Decimal form (going down, then across) a)15600 b)259 c)2.59 d)0.0056 e)0.0000459 f)0.0000209 g)0.0369 h)0.1369 i)73690000 j)69000 4.Calculate a)2.7 x 10 6 b)-2.7 x 10 3 c)2.53 x 10 24 d)1.47 x 10 3 e)2.2 x 10 6 f)-3.5 x 10 2 g)5.34 x 10 -44 h)-1.2 x 10 -2 Section 3 Using Scientific Measurements Chapter 2

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Class Starter 9/17. Check EQ and MV. Check your answers from the Sig Fig worksheet 5.Calculate a)2.63 x 10 -4 b)2.3 x 10 13 c)1.97 x 10 2 d)1.65 x 10 -23 e)2.5 x 10 -83 f)1.6 x 10 14 g)2.000 x 10 79 h)2.37 x 10 -7 Section 3 Using Scientific Measurements Chapter 2

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End of Chapter 2 Show

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