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Chapter 1

Chapter 1. Matter, Energy and Measurement. Scientific Method. The Scientific Method is the systematic investigation of natural phenomena where: Observations are explained in terms of general scientific principles Principles are formulated from hypotheses

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Chapter 1

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  1. Chapter 1 Matter, Energy and Measurement

  2. Scientific Method • The Scientific Method is the systematic investigation of natural phenomena where: • Observations are explained in terms of general scientific principles • Principles are formulated from hypotheses • Hypotheses are tested by further experimentation • Sufficient empirical support elevates hypothesis to theory or natural law

  3. In Science is there ALWAYS a “Right” answer? • Most of the calculations you will encounter in this course (i.e., the homework problems no known answer- they propose a “best” explanation and exams) have “right” answers • In “real life”, researchers investigate questions for which there is

  4. Scientific Notation • Scientific notation is a method of conveniently expressing extremely large or extremely small numbers. We will use scientific notation whenever dealing with large or small numbers.

  5. Scientific Notation • How to write numbers in scientific notation: • Find the decimal point. • Find the first non-zero digit (reading left to right). • Move the decimal point to the right of the first non-zero digit. Count the number of spaces moved. If the decimal point was moved to the left, the number of spaces moved is the positive exponent. If the decimal was moved right, it is the negative exponent. • Re-write the number with the decimal point in the new position. Drop all zeros to the left of the first non-zero digit. Drop all zeros to the right of the last non-zero digit only if the original number did not show the decimal.

  6. Scientific Notation • Distance to the moon = 380,000 km = 3.8 x 105 km • Distance to the sun = 150,000,000 km = 1.5 x 108 km • Diameter of a neuron = 0.00005 m = 5 x 10-5 m • Diameter of plutonium atom = 0.0000000003 m = 3 x 10-10 m • Number of water molecules in an drop = 1000000000000000000000 = 1 x 1021

  7. Scientific Notation • 180,000,000 g • 0.00006 m • 750,000 g • 0.15 m • 0.024 s • 1,500 m3

  8. Scientific Notation to Standard Numbers • How to take numbers out of scientific notation: • Write the number portion of the scientific notation expression, including the decimal point. (Do not include “times ten to the power of…”) • If the exponent is positive, move the decimal point to the right and move the number of spaces indicated by the exponent. If the exponent is negative, move the decimal point to the left. You will need to add zeros as you are moving the decimal point.

  9. Scientific Notation to Standard Numbers: Examples • 3.6 x 10-5 • 8.75 x 104 • 3 x 10-2 • 2.12 x 105

  10. Scientific Notation to Standard Numbers: Problems • Write the following as standard numbers: • 7.2 x 10-3 m • 2.4 x 105 g • 3.6 x 10-5 ml • 8.75 x 104 m

  11. Scientific Notation: Calculator Practice • (7.2 x 103) x (8.2 x 102) = 5904000 = 5.904 x 106 • (4.5 x 10-4) x (3.2 x 10-2) = 0.0000144 = 1.44 x 10-5 • (1 x 104) x (1 x 104) = 100000000 = 1 x 108 • (5.2 x 10-4) x (6.8 x 10-2) = 0.0000354 = 3.54 x 10-5

  12. Measured vs Exact Numbers • Measured numbers are those obtained from some type of measuring device, like a thermometer (which measures temperature) or a scale (which measures mass) or a ruler (which measures length). • Exact numbers are obtained from counting, like 12 eggs or 3 feet in a yard (conversions)

  13. Measured vs Exact Numbers • The difference between a measured number and an exact number is the certainty or uncertainty of the number. • Exact numbers are known with certainty. We are certain that there are exactly 12 eggs in a dozen. We do not wonder if there might really be 12.5 eggs, or 12.1 eggs. • Measured numbers have a certain amount of uncertainty. When we take a measurement, we always are limited by the sensitivity of our measuring device. Typically, the last digit expressed in a measured number is approximated and therefore uncertain.

  14. Measured vs Exact Numbers • Identify the following numbers as measured or exact and give the number of sig figs in each measured number: 42.2 g 3 eggs 0.0005 cm 450 000 km 3.500 x 105s

  15. Measured vs Exact Numbers • Identify the numbers in each of the following statements as measured or exact: • There are 31 students in the laboratory • The oldest known flower lived 120 000 000 years ago • The largest gem ever found has a mass of 104 kg • A laboratory test shows a blood cholesterol level of 184 mg/dL

  16. Measured vs Exact Numbers • In each of the sets of numbers, identify the exact number(s) if any: • 5 pizzas and 50.0 g of cheese • 6 nickels and 16 g of nickel • 3 onions and 3 lb of potatoes • 5 miles and 5 cars

  17. Significant Figures • Significant figures (“Sig Figs”) are all the certain digits in a measured number as well as the first uncertain digit. It is important for us to be able to recognize the significant figures of a number. When we multiply or divide numbers, there are rules that dictate how many digits in the answer are “Certain”

  18. Significant Figures

  19. Significant Figures • Significant figures: • All non-zero digits are significant. • All zeros in the middle of non-zero digits are significant. • All zeros at the end of a number with a written decimal point. • All digits written in scientific notation • Not significant figures: • All zeros at the beginning of any number. • All zeros at the end of a number written without a decimal point. The zero is used as a placeholder

  20. Significant Figures:Examples • 20.60 g • 1036.48 mL • 4.00 mg • 60,800,000 years

  21. Significant Figures:Problems • For each measurement, indicate if the zeros are significant: • 20.05 g • 5.00 m • 0.000 02 L • 120 000 years • 8.05 x 102 g

  22. Significant Figures:Problems • How many sig figs are in each of the following measured quantities: • 20.60 L • 1036.48 g • 4.00 m • 60 8000 000 g • 20.8 °C • 5.0 x 10-3 L

  23. Significant Figures:Problems • Write each of the following in scientific notation with 2 sig figs • 5 100 000 g • 26 000 s • 40 000 m • 0.000 820 kg • 0.000 004 5 m

  24. Rounding Numbers • When rounding a number, look to the digit immediately to the right of the last significant digit. • If that number (the number to the right) is 0, 1, 2, 3, or 4, simply drop all insignificant digits. • If that number (the number to the right) is 5, 6, 7, 8, or 9, round the last significant figure up and drop all significant digits.

  25. Significant Zeros • When a number needs to be expressed to more significant figures, add “significant zeros” to the right of the number. • If the number is a decimal, simply add more zeros to the right of the number. • If the number does not have a decimal, it is easiest to write the number in scientific notation (which requires you to write a decimal point) and then add zeros to the right of the number.

  26. Rounding-Examples • Re-write the following numbers to three significant digits. • 1.854 • 184.2038 • 0.004738265 • 8800

  27. Sig Figs in Calculations • Rule for multiplying and dividing: • Express the final answer to the lowest number of significant figures. • Rule for adding and subtracting: • Express the final answer to the lowest number of decimal places

  28. Sig Figs in Calculations:Examples • Perform the following calculations and express the answer to the proper number of sig figs: • 45.7 x 0.034 • 0.00278 x 5 • 34.56 x 1.25 • (0.2465 x 25) x 1.78

  29. Sig Figs in Calculations:Examples • Perform the following calculations and express the answer to the proper number of sig figs: • 45.48 + 8.057 • 23.45 + 104.1 + 0.025 • 145.675 – 24.2 • 1.08 – 0.585

  30. Sig Figs in Calculations:Problems • Round off each of the following numbers to three sig figs: • 35.7823 m • 0.002627 L • 3826.8 g • 1.2836 kg

  31. Sig Figs in Calculations:Problems • Perform the following calculations of measured numbers. Give the answers with the correct number of sig figs: • 56.8 x 0.37 • 71.4/11 • (2.075 x 0.585)/(8.42 x 0.00450) • 25.0/5.00

  32. Sig Figs in Calculations:Problems • Perform the following calculations and give the answers with the correct number of decimal places: • 27.8 cm + 0.235 cm • 104.45 mL + 46 mL + 0.838 mL • 153.247 g - 14.82 g

  33. Sig Figs in Calculations:Problems • Round off each of the following numbers to three sig figs: • 1.854 • 184.2038 • 0.004738265 • 8807 • 1.832149 • Round the numbers above to 2 sig figs:

  34. Sig Figs in Calculations:Problems • For the following calculations, give answers with the correct number of significant figures: • 400 x 185 • 2.40/(4 x 125) • 0.825 x 3.6 x 5.1 • (3.5 x 0.261)/(8.24 x 20.0)

  35. Sig Figs in Calculations:Problems • For the following calculations, give answers with the correct decimal places: • 5.08 cm + 25.1 cm • 85.66 cm + 104.10 cm + 0.025 cm • 24.568 mL - 14.25 mL • 0.2654 L - 0.2585 L

  36. Practice Problems • Problem 1.1 page 9

  37. The Metric System of Measurement DIMENSION COMMON UNITSYMBOL Mass gramg Length meterm Time seconds Temperature kelvin K deg CelsiusºC Volume literL

  38. The Metric System • Three nations have not officially adopted the International System of Units as their primary or sole system of measurement: Burma, Liberia and the United States

  39. Length • Distance from one point to another • US Customary Units: Inch, foot, yard, mile • Metric Units: Meter, centimeter, millimeter, kilometer, etc. • SI Unit: Meter

  40. Volume • Amount of space an object occupies • US Customary Units: Pint, quart, gallon, etc. • Metric Units: Liter, milliliter, cubic centimeter, etc. • SI Unit: Cubic meter

  41. Mass • Quantity of an object (note that mass and weight are not the same!) • US Customary Units: Pound, ounce, ton, etc. • Metric Units: Gram, kilogram, etc. • SI (International System of Units) Unit: Kilogram

  42. Time • US Customary Unit: Second, minute, hour, day, etc. • Metric Unit: Second, millisecond, etc. • SI Unit: Second

  43. Temperature • Measurement of the heat of an object • US Customary Unit: Degrees Fahrenheit • Metric Unit: Degrees Celsius • SI Unit: Kelvin

  44. Three Temperature Scales

  45. The Metric System:Metric prefixes Prefix Symbol Multiple Example nano n 10-9 nm (molecule size) micro m 10-6mm (cell size) milli m 10-3 mL (flu shot) centi c 10-2 cm (ski length) kilo k 103 kg (weights) mega M 106 MW (power) giga G 109 GB (memory)

  46. Prefixes • Prefixes are added to metric base units to increase or decrease the metric unit by some factor of ten. • Liter is the base unit of volume. • Gram is the base unit of mass. • Meter is the base unit of length. • Table 1.2 Page 9: All prefixes must be memorized, including the symbol and numerical value.

  47. Equalities • Equalities are set of numbers which are mathematically equal, but expressed in different units. For example, 12 inches = 1 foot. • 1 m = ____ cm • 1 km = ____ m • 1 mm = ____ m • 1 L = ____ mL

  48. Prefixes and Equalities:Problems • Fill in the blanks with the correct numerical value: • Kilogram = _____ grams • Millisecond = _____ second • Deciliter = _____ Liter

  49. Prefixes and Equalities:Problems • Complete the following list of metric equlaities: • 1 L = _____ dL • 1 km = _____ m • 1 m = _____ cm • 1 cm3 = _____ mL

  50. Prefixes and Equalities:Problems • Write the abbreviation for each of the following units: • Milligram • Deciliter • Kilometer • Kilogram • microliter

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