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 10 8 Coefficient Superscript

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 10 5 – 5.4 x 10 -5 – 5.060 x 10 3 – 8.9 x 10 -7

7. Significant Figures all the digits that are known precisely plus one last one that is estimated.

8. Rules for Significant Digits 1.Every nonzero digit is significant Ex. 24.7 m 2.Zeros appearing between nonzero digits are significant Ex. 24.07 m

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

10. 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 10 3

11. 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!

12. 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

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

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

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

16. 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

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

18. Temperature Scales Fahrenheit – Water freezes at – Water boils at – o F = 1.8( o C) + 32 Celsius – Water freezes at – Water boils at – o C = ( o F – 32)/1.8

19. Which is warmer, 25 o F or 25 o C? What is 98 o F in o C? What is 20 o C in o F?

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

21. – What is 25 o C in K? – What is 300 K in o C? – What is 35 o F in K?

22. Derived Units Derived unit – unit that is made by combining two or more base units – m/s – g/mL – cm 3

23. Volume – space an object takes up – L x w x h – SI unit – m 3 – More useful unit = L 1 L = 1 dm 3 1 mL = 1 cm 3

24. 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?

25. Density = amount of mass per unit volume – g/cm 3 – g/mL – kg/L Always the same for a given substance – D = M/V

26. What is the density of a cube that has a mass of 20 g and a volume of 5 cm 3 ?

27. 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?

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

29. 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

30. 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

31. Convert 100 yards to feet Convert 5 kilometers to miles

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

33. Convert 3,000,000 s to years

34. Conversions with derived units Convert 365 mm 3 to m 3 Convert 15.9 cm 3 /s to L/h

35. Convert 25 miles/hour to ft/second Convert 1.004 g/cm 3 to kg/mL

36. Uncertainty in Data All measurements contain uncertainties

37. 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

38. 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

39. Precise Accurate

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

41. 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?

42. 2.4 Representing Data Graphs are a visual representation of data which make it easier to see patterns and trends

43. Circle graphs Aka – Show parts of a fixed whole

44. Bar Graphs Show how a quantity varies across categories Y axis – X axis –

45. Line Graphs Points on line = intersection of data for independent and dependent variable Y axis – X axis –

46. Relationship between variables can be analyzed by the slope of the line. – Slope = – + slope = – - slope =

47. Interpreting Graphs 1.What is the independent variable 2.What is the dependent variable 3.Is the relationship linear? 4.Is the slope positive or negative

48. Interpolation – reading data from any point that falls between recorded data points

49. Extrapolation – extending line beyond data points to estimate future values – Be careful! Can easily lead to errors