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Chapter 2 - Measurements and Calculations

Chapter 2 - Measurements and Calculations. Section 2.1 - Scientific Method Read Section 1 - Going Through Very Quickly. Observing and Collecting Data Quantitative - Numerical Information (25.7 grams) Qualitative - Non-numerical (the fact that the sky is blue)

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Chapter 2 - Measurements and Calculations

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  1. Chapter 2 - Measurements and Calculations Chapter 2 - Measurements and Calculations

  2. Section 2.1 - Scientific MethodRead Section 1 - Going Through Very Quickly • Observing and Collecting Data • Quantitative - Numerical Information (25.7 grams) • Qualitative - Non-numerical (the fact that the sky is blue) • A system is a specific portion of matter in a given region of space that has been selected for study during and experiment or observation Chapter 2 - Measurements and Calculations

  3. Scientific Method Cont- • Formulating Hypothesis • Scientists use generalizations about data to formulate a hypothesis, or testable statement. • The hypothesis serves as a basis for making predictions and for carrying out further experiments • Hypothesis are “if-then” statements Chapter 2 - Measurements and Calculations

  4. Scientific Method Cont- • Theorizing • When data shows the predictions of the hypothesis to be successful,Scientists try to explain by constructing a model. • A model is a physical object built to explain a hypothesis. • If a model successfully explains the data then it becomes part of a theory, which is a broad generalization that explains a body of facts. Chapter 2 - Measurements and Calculations

  5. Section 2-2 Units of Measurement Observations are either: Quantitative - Numerical Information (25.7 grams) Qualitative - Non-numerical (the fact that the sky is blue) A system is a specific portion of matter in a given region of space that has been selected for study during and experiment or observation Measurements represent quantities. A quantity is something that has magnitude, size, or amount. Measurements are numbers plus a unit. Measurements are quantitative! Chapter 2 - Measurements and Calculations

  6. What are units? • Units are descriptors of numbers. • They give numbers meanings. • For example, the ordinary number 30. • You have no clue what the number 30 represents, it could be 30 desks, 30 pencils, or 30 books. • You need a descriptor or a unit to tell you exactly what the number represents. • For instance, 300C, tells us that 30 represents a temperature. • Or, 30 meters tells us that 30 is representing a distance or a length. Chapter 2 - Measurements and Calculations

  7. The Metric System • The metric system of measurement has a long historical background and grew out of a need for standard and reproducible measurement for both science and commerce. • It has two advantages over the English system of measurement. 1. Units are well defined in terms of things that are easily and accurately reproduced. 2. All conversions within the system can be preformed by moving a decimal point. Chapter 2 - Measurements and Calculations

  8. SI Measurement • In 1960, modern SI Units were established. • Scientists all over the world have agreed on a single measurement system called • “Le Systeme International de Unites”, abbreviated SI. • This revision declared that only a minimum number of base units would be rigorously defined. • These base units are…….. Chapter 2 - Measurements and Calculations

  9. There are Seven Base Units the meter(m) for distance or length, the kilogram(kg) for mass the second(s) for time the ampere(A) for electric current the Kelvin(K) for temperature the mole(mol) for amount of substance the candela for intensity of light. All other units would be derived from these base units!!!!!!! Chapter 2 - Measurements and Calculations

  10. Prefixes • There are several prefixes that are associated with a decimal position and can be attached to a base metric unit in order to create a new metric unit. • The knowledge of the decimal meaning of the prefix establishes the relationship between the newly created unit and the base unit. • Page 35 in your text. Similar Chart on next slide Chapter 2 - Measurements and Calculations

  11. Chapter 2 - Measurements and Calculations

  12. Metric Conversion - The Factory Label Method (SHOW YOUR WORK!) METRIC UNIT TO BASE 2.5 cm = _______ m We know that 1m = 100 cm, so possible conversion factors are: 1m/100cm or 100cm/1m , which do I choose? 2.5 cm X 1m 100 cm = 0.025 m I choose 1m/100cm because I needed cm to cancel out and needed to end up with the units of meter! Chapter 2 - Measurements and Calculations

  13. Another Example - BASE TO METRIC UNIT 34 L = ___________ ml I know that there are 1000ml in 1 L, so I have the choice between two conversion factors 1000ml/1L or 1L/1000ml, so I look @ the conversion and decide which one will allow me to cancel out L and end up with ml in my final answer. 34 L X 1000ml 1L = 34,000 ml Chapter 2 - Measurements and Calculations

  14. Unit Conversion Examples - Show your work!!!! METRIC TO BASE TO METRIC 85.6 mg to kilograms 85.6 mg x 1g x 1kg = 0.0000856 1000mg 1000g 85.6 mg x 1kg = 0.0000856 106mg 79.3 hectoliters to milliliters 79.3 hL x 100L x 1000ml = 7,930,000 ml 1hL 1L Chapter 2 - Measurements and Calculations

  15. Scientific Notation In scientific notation, numbers are written in the form M x 10n Where M is a number greater than or equal to 1 but less than 10 and n is a whole number Chapter 2 - Measurements and Calculations

  16. Rules for Scientific Notation • Scientific Notation is a short cut for writing very large or very small numbers • Long form (regular numbers) to Scientific Notation • 1. Is the number greater or less than 1 • 2. If it is not already, you want to position the decimal point where the number to the left is less than 10, but greater than 0 • 3. When moving the decimal from the original position to the position described in Rule 2, notice which way the point moves • a. To the right– the power or exponent of 10 will be negative • b. To the left– the exponent will be positive • 4. How many places the decimal point moves is the power of 10 • Example: • 0.00045 – 4.5 x 10-4 456789 – 4.6 x 105 Chapter 2 - Measurements and Calculations

  17. Scientific Notation to Long form • If the exponent is negative move the decimal to the left • 2. If it is positive move it to the right • Example: 2.6 x 10-3– 0.0026 • 3.94 x 104 - 39400 Chapter 2 - Measurements and Calculations

  18. Mathematical Operations and Scientific Notation Calculator Operation – Will go over in class! • By Hand – I strongly suggest using your calculators for accuracy!!! • Addition/Subtraction Using Scientific Notation • Convert the numbers to the same power of ten, usually the largest. • Add (subtract) the nonexponential portion of the numbers. • The power of ten remains the same. • Example: (1.00 × 104) + (2.30 × 105) • A good rule to follow is to express all numbers in the problem • to the highest • power of ten. • Convert (1.00 × 104) to (0.100 × 105). • (0.100 ×105) 1 (2.30 × 105) = 2.40 × 105 Chapter 2 - Measurements and Calculations

  19. Multiplication Using Scientific Notation • The numbers (including decimals) are multiplied. • The exponents are added. • The answer is converted to scientific notation—the product of a number between 1 and 10 and an exponential term. • Example: (4.24 × 102) × (5.78× 104) • (4.24 × 5.78) × (102+4) = 24.5 × 106 • Convert to scientific notation = 2.45 × 107 • Division Using Scientific Notation • 1. Divide the decimal parts of the number. • 2. Subtract the exponents. • 3. Express the answer in scientific notation. • Example: (3.78 × 105) / (6.2 × 108) • (3.78 × 6.2) × (105-8) = 0.61 × 10-3 • Convert to scientific notation = 6.1 × 10-4 Chapter 2 - Measurements and Calculations

  20. Derived SI Units • Combinations of SI base units form derived units. • Derived units are produced by multiplying or dividing standard units. • Examples (2m)(2m) = 4 m2 (meters squared) 2g = 1 g/ml (grams per milliliter) 2ml A this per that number!!. There is 1 g of substance for every 1 ml. Chapter 2 - Measurements and Calculations

  21. Using Scientific Measurements • Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. (ATV) • Precision refers the closeness of a set of measurements of the same quantity made in the same way. Chapter 2 - Measurements and Calculations

  22. Accuracy vs. Precision Accepted value is the bulls eye Chapter 2 - Measurements and Calculations

  23. These values were recorded as the mass of products when a chemical reaction was carried out three separate times: 8.83 g; 8.84 g; 8.82 g. The mass of products from that reaction is 8.60 g (Accepted Value). Are the experimental values accurate, precise, or both? 8.83g, 8.84g, and 8.82g are measurements that are very close to one another! They are PRECISE!!!! 8.60 g = the accepted agreed upon value for the reaction In a laboratory setting 0.20 g is a significant deviation from the accepted value! They too far from the accepted value thus inaccurate! The Experiment produced Precise, but inaccurate results!!! Chapter 2 - Measurements and Calculations

  24. Percent Error • Percent Error is calculated by subtracting the experimental value from the accepted value, dividing the difference by the accepted value, and then multiplying by 100. • Percent Error = (Value experimental - Valueaccepted) X 100 Value accepted Chapter 2 - Measurements and Calculations

  25. Errors in Measurement • Some error or uncertainty exists in any measurement • WHY? Skill of the measurer The conditions The measurement instrument themselves Chapter 2 - Measurements and Calculations

  26. Significant Figures 11.65 inches • Sig Figs in a measurement consists of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. • The rules for determining sig figs are located on page 47. 11.6 for certain + 5 which is estimated for a measurement of - 11.65 inches Chapter 2 - Measurements and Calculations

  27. Rule 1 0.0032 - 2 sig figs (Rule 2) Remember: Zeros between Non zero numbers are Significant. 45.00 - 4 sig figs (Rule 3) Ex. 45689 - 5 sig figs (Rule 1) Ex: 3200 2 sig figs (Rule 4) Chapter 2 - Measurements and Calculations

  28. Rules for Sig Figs By Examples Rule 1 80.67 = 4 20487 = 5 67009 = 5 12 = 2 198762534 =9 4 = 1 Rule 2 0.0567 = 3 0.000001 = 1 0.034 = 2 0.01234567 = 7 0.000000023 = 2 0.12 = 2 Chapter 2 - Measurements and Calculations

  29. Rules By Example continued Rule 3 4.00 = 3 234.00 = 5 12389.000 = 8 1.20 = 3 2.4500 = 5 Rule 4 2000 = 1 2340000 = 3 1200 = 2 1200. = 4 2000. = 4 Chapter 2 - Measurements and Calculations

  30. Addition, Subtraction, and Division with Sig Figs • When adding, subtracting, or dividing numbers, determine the number that has the least number of sig figs and record (round) your answer to that number of sig figs. Chapter 2 - Measurements and Calculations

  31. Direct Proportions • Two quantities are directly proportional to each other if dividing one by the other gives a constant value • As one quantity increases so does the other • Graph is in the shape of a straight Line Chapter 2 - Measurements and Calculations

  32. Inverse Proportions • Two quantities are inversely proportional to each other if their product is constant • As one goes up the other goes down • Graph is a hyperbola Chapter 2 - Measurements and Calculations

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