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Analyzing Data. Section 2.1 Units and Measurements Section 2.2 Scientific Notation and Dimensional Analysis Section 2.3 Uncertainty in Data Section 2.4 Representing Data. Click a hyperlink or folder tab to view the corresponding slides. Exit. Chapter Menu.

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  1. Analyzing Data Section 2.1Units and Measurements Section 2.2Scientific Notation and Dimensional Analysis Section 2.3Uncertainty in Data Section 2.4Representing Data Click a hyperlink or folder tab to view the corresponding slides. Exit Chapter Menu

  2. Section 2.1 Units and Measurements • Define SI base units for time, length, mass, and temperature. • Explain how adding a prefix changes a unit. • Compare the derived units for volume and density. mass: a measurement that reflects the amount of matter an object contains Section 2-1

  3. Section 2.1 Units and Measurements (cont.) base unit second meter kilogram kelvin derived unit liter density Chemists use an internationally recognized system of units to communicate their findings. Section 2-1

  4. Units • Système Internationale d'Unités (SI) is an internationally agreed upon system of measurements. • A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units. Section 2-1

  5. Units (cont.) Section 2-1

  6. Units (cont.) Section 2-1

  7. Units (cont.) • The SI base unit of time is the second (s), based on the frequency of radiation given off by a cesium-133 atom. • The SI base unit for length is the meter (m), the distance light travels in a vacuum in 1/299,792,458th of a second. • The SI base unit of mass is the kilogram (kg), about 2.2 pounds Section 2-1

  8. Units (cont.) • The SI base unit of temperature is the kelvin(K). • Zero kelvin is the point where there is virtually no particle motion or kinetic energy, also known as absolute zero. • Two other temperature scales are Celsius and Fahrenheit. Section 2-1

  9. Derived Units • Not all quantities can be measured with SI base units. • A unit that is defined by a combination of base units is called a derived unit. Section 2-1

  10. Derived Units (cont.) • Volume is measured in cubic meters (m3), but this is very large. A more convenient measure is the liter, or one cubic decimeter (dm3). Section 2-1

  11. Derived Units (cont.) • Density is a derived unit, g/cm3, the amount of mass per unit volume. • The density equation is density = mass/volume. Section 2-1

  12. A B C D Section 2.1 Assessment Which of the following is a derived unit? A.yard B.second C.liter D.kilogram Section 2-1

  13. A B C D Section 2.1 Assessment What is the relationship between mass and volume called? A.density B.space C.matter D.weight Section 2-1

  14. End of Section 2-1

  15. Section 2.2 Scientific Notation and Dimensional Analysis • Express numbers in scientific notation. • Convert between units using dimensional analysis. quantitative data: numerical information describing how much, how little, how big, how tall, how fast, and so on Section 2-2

  16. Section 2.2 Scientific Notation and Dimensional Analysis (cont.) scientific notation dimensional analysis conversion factor Scientists often express numbers in scientific notation and solve problems using dimensional analysis. Section 2-2

  17. Scientific Notation • Scientific notation can be used to express any number as a number between 1 and 10 (the coefficient) multiplied by 10 raised to a power (the exponent). • Count the number of places the decimal point must be moved to give a coefficient between 1 and 10. Section 2-2

  18. Scientific Notation (cont.) • The number of places moved equals the value of the exponent. • The exponent is positive when the decimal moves to the left and negative when the decimal moves to the right. 800 = 8.0  102 0.0000343 = 3.43  10–5 Section 2-2

  19. Scientific Notation (cont.) • Addition and subtraction • Exponents must be the same. • Rewrite values with the same exponent. • Add or subtract coefficients. Section 2-2

  20. Scientific Notation (cont.) • Multiplication and division • To multiply, multiply the coefficients, then add the exponents. • To divide, divide the coefficients, then subtract the exponent of the divisor from the exponent of the dividend. Section 2-2

  21. Dimensional Analysis • Dimensional analysis is a systematic approach to problem solving that uses conversion factors to move, or convert, from one unit to another. • A conversion factor is a ratio of equivalent values having different units. Section 2-2

  22. Dimensional Analysis (cont.) • Writing conversion factors • Conversion factors are derived from equality relationships, such as 1 dozen eggs = 12 eggs. • Percentages can also be used as conversion factors. They relate the number of parts of one component to 100 total parts. Section 2-2

  23. Dimensional Analysis (cont.) • Using conversion factors • A conversion factor must cancel one unit and introduce a new one. Section 2-2

  24. A B C D Section 2.2 Assessment What is a systematic approach to problem solving that converts from one unit to another? A.conversion ratio B.conversion factor C.scientific notation D.dimensional analysis Section 2-2

  25. A B C D Section 2.2 Assessment Which of the following expresses 9,640,000 in the correct scientific notation? A.9.64  104 B.9.64  105 C.9.64 × 106 D.9.64  610 Section 2-2

  26. End of Section 2-2

  27. Section 2.3 Uncertainty in Data • Define and compare accuracy and precision. • Describe the accuracy of experimental data using error and percent error. • Apply rules for significant figures to express uncertainty in measured and calculated values. experiment: a set of controlled observations that test a hypothesis Section 2-3

  28. Section 2.3 Uncertainty in Data (cont.) accuracy precision error percent error significant figures Measurements contain uncertainties that affect how a result is presented. Section 2-3

  29. Accuracy and Precision • Accuracy refers to how close a measured value is to an accepted value. • Precision refers to how close a series of measurements are to one another. Section 2-3

  30. Accuracy and Precision (cont.) • Erroris defined as the difference between and experimental value and an accepted value. Section 2-3

  31. Accuracy and Precision (cont.) • The error equation is error = experimental value – accepted value. • Percent errorexpresses error as a percentage of the accepted value. Section 2-3

  32. Significant Figures • Often, precision is limited by the tools available. • Significant figures include all known digits plus one estimated digit. Section 2-3

  33. Significant Figures (cont.) • Rules for significant figures • Rule 1: Nonzero numbers are always significant. • Rule 2: Zeros between nonzero numbers are always significant. • Rule 3: All final zeros to the right of the decimal are significant. • Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation. • Rule 5: Counting numbers and defined constants have an infinite number of significant figures. Section 2-3

  34. Rounding Numbers • Calculators are not aware of significant figures. • Answers should not have more significant figures than the original data with the fewest figures, and should be rounded. Section 2-3

  35. Rounding Numbers (cont.) • Rules for rounding • Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure. • Rule 2: If the digit to the right of the last significant figure is greater than 5, round up to the last significant figure. • Rule 3: If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up to the last significant figure. Section 2-3

  36. Rounding Numbers (cont.) • Rules for rounding (cont.) • Rule 4: If the digits to the right of the last significant figure are a 5 followed by a 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even, do not round up. Section 2-3

  37. Rounding Numbers (cont.) • Addition and subtraction • Round numbers so all numbers have the same number of digits to the right of the decimal. • Multiplication and division • Round the answer to the same number of significant figures as the original measurement with the fewest significant figures. Section 2-3

  38. A B C D Section 2.3 Assessment Determine the number of significant figures in the following: 8,200, 723.0, and 0.01. A.4, 4, and 3 B.4, 3, and 3 C.2, 3, and 1 D.2, 4, and 1 Section 2-3

  39. A B C D Section 2.3 Assessment A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is the percent error? A.0.20 g/L B.–0.20 g/L C.0.10 g/L D.0.90 g/L Section 2-3

  40. End of Section 2-3

  41. Section 2.4 Representing Data • Create graphics to reveal patterns in data. independent variable: the variable that is changed during an experiment • Interpret graphs. graph Graphs visually depict data, making it easier to see patterns and trends. Section 2-4

  42. Graphing • A graphis a visual display of data that makes trends easier to see than in a table. Section 2-4

  43. Graphing (cont.) • A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole. Section 2-4

  44. Graphing (cont.) • Bar graphs are often used to show how a quantity varies across categories. Section 2-4

  45. Graphing (cont.) • On line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the y-axis. Section 2-4

  46. Graphing (cont.) • If a line through the points is straight, the relationship is linear and can be analyzed further by examining the slope. Section 2-4

  47. Interpreting Graphs • Interpolation is reading and estimating values falling between points on the graph. • Extrapolation is estimating values outside the points by extending the line. Section 2-4

  48. Interpreting Graphs (cont.) • This graph shows important ozone measurements and helps the viewer visualize a trend from two different time periods. Section 2-4

  49. A B C D Section 2.4 Assessment ____ variables are plotted on the ____-axis in a line graph. A.independent, x B.independent, y C.dependent, x D.dependent, z Section 2-4

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