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Chapter 2

Chapter 2. Analyzing Data. Scientific Notation & Dimensional Analysis. Scientific notation – way to write very big or very small numbers using powers of 10 3 x 10 8. Superscript. Coefficient. Superscript Rules. Numbers greater than 10 = Ex. 257000000000000 Numbers less than 10 =

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Chapter 2

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  1. Chapter 2 Analyzing Data

  2. Scientific Notation & Dimensional Analysis • Scientific notation – way to write very big or very small numbers using powers of 10 3 x 108 Superscript Coefficient

  3. Superscript Rules • Numbers greater than 10 = • Ex. 257000000000000 • Numbers less than 10 = • Ex. 0.0000000000000257

  4. Rules for Scientific Notation • The coefficient must be between 1.0 and 9.99. • Your coefficient must contain all significant digits. • Move the decimal point as many places as necessary until you create a coefficient between 1.0 and 9.99. • The exponent will be the number of places you move your decimal point. • Moving the decimal to the left makes the number larger = POSITIVE EXPONENT • Numbers greater than 10 always have exponents that are positive. • Moving the decimal to the right makes the number smaller = NEGATIVE EXPONENT • Numbers less than 1.0 always have exponents that are negative

  5. Write the following in scientific notation • 1,392,000 km • 0.0000000028 • 1176.9 • 0.0123

  6. Write the following in regular notation • 3.6 x 105 • 5.4 x 10-5 • 5.060 x 103 • 8.9 x 10-7

  7. Uncertainty in Measurement

  8. Uncertainty in Measurement • A measurement always has some degree of uncertainty.

  9. Different people estimate differently. • Record all certain numbers and one estimated number.

  10. Significant Figures • Numbers recorded in a measurement. • All the certain numbers plus first estimated number

  11. Rules for Significant Digits • Every nonzero digit is significant Ex. 24.7 m • Zeros appearing between nonzero digits are significant Ex. 24.07 m

  12. 3. Zeros after significant digits are only significant if there is a decimal point Ex. 2470 Ex. 2470.0

  13. 4. Zeros in front of numbers are NOT significant, even after a decimal point Ex. 0.0000247 Ex. 0.247 5. When a number is in scientific notation, all numbers in the coefficient are significant Ex. 2.470 x 103

  14. Significant Digits in Calculations • An answer cannot be more precise than the least precise measurement from which it was calculated. • To round off an answer you must first decide how many significant digits the answer should have. • Your calculator DOES NOT keep track of significant digits, you have to do it!

  15. Addition & Subtraction • Answer can have no more decimal places than the number in the problem with the fewest decimal places. • Ex: 4.5 + 6.007 + 13.39 = 23.897 • Correct sig figs = 23.9

  16. Multiplication & Division • Answer can have no more significant digits than the number in the problem with the fewest significant digits • Ex: 3.24 x 7.689 x 12.0 = 298.94832 • Correct Sig. Figs = 299

  17. Units and Measurement • Systeme Internationale d’Unites (SI Units) – standard units of measure used by all scientists. • Why?

  18. Base Units and SI Prefixes • Base unit – measurements that can be taken with one instrument • Time • Length • Mass • Temperature • Amount

  19. Prefixes are added to base units to indicate very large or very small quantities.

  20. Second – determined by the frequency of radiation given of by cesium – 133 • Meter – distance light travels in a vacuum in 1/299,792,458 of a second • Kilogram – defined by a platinum and iridium cylinder kept in France

  21. Temperature – quantitative measurement of the average kinetic energy of the particles that make up an object

  22. Temperature Scales • Fahrenheit • Water freezes at • Water boils at • oF = 1.8(oC) + 32 • Celsius • Water freezes at • Water boils at • oC = (oF – 32)/1.8

  23. Which is warmer, 25 oF or 25 oC? • What is 98 oF in oC? • What is 20 oC in oF?

  24. Kelvin • Water freezes at 273 • Water boils at 373 • Theoretically molecule movement completely stops at 0 K (absolute zero) • K = C + 273

  25. What is 25 oC in K? • What is 300 K in oC? • What is 35 oF in K?

  26. Derived Units • Derived unit – unit that is made by combining two or more base units • m/s • g/mL • cm3

  27. Volume – space an object takes up • L x w x h • SI unit – m3 • More useful unit = L • 1 L = 1 dm3 • 1 mL = 1 cm3

  28. Volumes of irregular objects can be found by placing them into a graduated cylinder and measuring the amount of water that is displaced • What is the volume of the dinosaur?

  29. Density = amount of mass per unit volume • g/cm3 • g/mL • kg/L • Always the same for a given substance • D = M/V

  30. What is the density of a cube that has a mass of 20 g and a volume of 5 cm3?

  31. When a piece of aluminum is placed in a 25 mL graduated cylinder that contains 10.5 mL of water, the water level rises to 13.5 mL. The density of aluminum is 2.7 g/mL. What is the mass of the piece of aluminum?

  32. What is the volume of an object with a mass of 13.5 g and a density of 1.4 g/mL?

  33. Dimensional Analysis • A systematic approach to problem solving that uses conversion factors to move from one unit to another • Conversion factor is a ratio of equivalent values with different units • 1 km = 1000 m • 12 inches = 1 foot

  34. Tools for Problem Solving • Be systematic • Ask yourself these questions • Where do we want to go? • What do we know? • How do we get there? • Does it make sense?

  35. Tools for Problem Solving • Tools for Converting from One Unit to Another Step 1 Find an equivalence statement that relates the 2 units.Step 2 Choose the conversion factor by looking at the direction of the required change (cancel the unwanted units).Step 3 Multiply the original quantity by the conversion factor. Step 4 Make sure you have the correct number of significant figures.

  36. 1 step conversions Ex 1: A roll of wire is 15m long, what is the length in cm? Ex 2: convert 8.96L to milliliters

  37. Convert 100 yards to feet • Convert 5 kilometers to miles

  38. Multi step conversions • Convert 525 km to cm • Convert 10000 in to miles

  39. Convert 3,000,000 s to years

  40. Conversions with derived units • Convert 365 mm3 to m3 • Convert 15.9 cm3/s to L/h

  41. Convert 25 miles/hour to ft/second • Convert 1.004 g/cm3 to kg/mL

  42. Uncertainty in Data • All measurements contain uncertainties

  43. Accuracy vs. precision • Accuracy is how close a single measurement comes to the actual dimension or true value of what is measured • 4.555555 vs. 4.56 • More decimal places make a measurement more accurate. • Depends on quality of measuring device

  44. Precision is how close several measurements are to the same value • Depends on more than one measurement • Depends on the skill of the person making the measurement

  45. Precise Accurate

  46. Error and percent error • Experimental value – value measured during experiment • Accepted value – true or known value • Error = experimental value – accepted value

  47. Percent error: • You calculate the density of sucrose to be 1.40 g/mL. The accepted value for the density of sucrose is 1.59 g/mL. What is your % error?

  48. 2.4 Representing Data • Graphs are a visual representation of data which make it easier to see patterns and trends

  49. Circle graphs • Aka – • Show parts of a fixed whole

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