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Chapter 2: A Mathematical Toolkit

Chapter 2: A Mathematical Toolkit. Dr. Zalesinsky . The Metric System . Length or distance is measured in meters Mass is measured in grams Volume or capacity is measured in liters Time is measured in seconds Energy is measured in Joules Temperature is measured in Kelvin (not degrees)

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Chapter 2: A Mathematical Toolkit

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  1. Chapter 2: A Mathematical Toolkit Dr. Zalesinsky

  2. The Metric System • Length or distance is measured in meters • Mass is measured in grams • Volume or capacity is measured in liters • Time is measured in seconds • Energy is measured in Joules • Temperature is measured in Kelvin (not degrees) • Quantity is measured in moles

  3. The Liter (L)

  4. The Meter (m)

  5. Gram (g)

  6. The really small and really large Scientific Notation

  7. Scientific Notation

  8. Scientific Notation Examples • Change to Scientific Notation: 985,000,000 0.0000674 9.85 x 108 6.74 x 10-5 Change to Standard Notation: 8.27 x 106 9.565x10-2 8,270,000 .09565

  9. Using Scientific Notation with Calculator

  10. TI Graphing Calculator

  11. Examples • Do this calculation: (don’t type in the “x 10 part—use the EE or EXP button) Multiply:(8.76 x 10-10 )(7.9 x1011) = 692 or 6.92x102 Divide: (9.43x1043)/(7.33x1023) = (approximate) 1.3 x1020 be careful to turn your display into correct scientific notation 1.320 is not the same!

  12. Uncertainty in Measurement Significant Figures

  13. Which is larger? Meter or yard Mile or Kilometer Gallon or liter Pound or gram Quart or liter Centimeter or inch Gram or ounce What is the abbreviation for each unit? Meter = _____ Gram = _____ Liter = ______ Second = ______ Joule = _______ Mole = _______ English to Metric Comparisons

  14. The BASE units for the metric system are gram, liter, meter, second, Kelvin, Joule and mole. There are larger and smaller portions of each of these Their abbreviations come in front of the unit’s abbreviation (ex. centimeter = cm) Metric Abbreviations

  15. Larger 1 billion = GIGA (G) 1 million = MEGA (M) 1,000 = kilo (k) 100 = hecto (h) 10 = deca (D, dk, or da) Smaller 1trillion = pico (p) 1 billion = nano (n) 1 million = micro (m) 1,000 = milli (m) 100 = centi (c ) 10 = deci (d) Larger and Smaller Prefixes

  16. Cm = ________ mg = ________ ML = ________ Gg = ________ ms = ________ km = _______ mL = _______ kJ = ________ mm= _______ Dg = _______ Centimeter Milligram Megaliter Gigagram Microsecond Kilometer Milliliter Kilojoule Millimeter Decagram Match the abbreviation with the name

  17. Conversions

  18. Conversions

  19. Significant Figures • Read the correct number of significant figures

  20. Measure the following using significant figures

  21. Use Sig. Figs to find this measurement

  22. Use the correct number of sig. figs in this measurement

  23. What digit would be estimated in using Ruler A? • Ones • Tenths • Hundredths • Thousandths • Tens

  24. What decimal place is estimated when using Ruler B? • Ones D. Thousandths • Tenths E. Tens • Hundredths

  25. Measure the width of the rectangle using the correct number of sig figs. • 3. 75 cm D. 3.60 cm • 3.6 cm E. 4.25 cm • 2. 6 cm

  26. Measure the length of the rectangle using the correct number of sig figs. • 12.55 cm C. 12.0 cm E. 13.50 cm • 12. 5 cm D. 13. 5 cm

  27. How many sig figs should be in the correct measurement of the length of this rectangle? • 2 sig figs C. 4 sig figs E. 1 sig fig • 3 sig figs D. 5 sig figs

  28. The width of this rectangle is 0.90 cm. How many significant figures are in this measurement? • 3 sig figs D. infinite sig figs • 2 sig figs E. none of the above • 1 sig fig

  29. Data Table 1.1

  30. Data Table 1.2

  31. Data Table 1.5

  32. Data Table 1.6

  33. Calculating with Uncertainty Calculations with Significant figures

  34. Multiplication and Division with Sig Figs • The least number of sig figs in the input is equal to the number of sig figs in the answer (output). • Remember all conversion factors and counted numbers have INFINITE sig figs! • Example: 8.03 g x 4.0 cm3/g = ?

  35. Addition and Subtraction with Sig Figs • The least number of decimal places in the input is the same number of decimal places in the output (answer). • 12.573 m + 3847.9 m - 378 m = ? • 3482.473 (unrounded) • 3482 rounded to the correct number of decimal places

  36. Calculations with Sig Figs • A rectangle has a width of 5.0 cm and a length of 8.40 cm. What is the area of this rectangle in cm2? ___________ • A rectangular prism has the following measurements: length 8.54 cm, width 7.80cm, and height 10.00 cm. What is the volume in cm3? ______________

  37. Data Table 1.2 Data Table 1.3

  38. Data Table 1.6 Data Table 1.7

  39. 2.3 Visualizing Data

  40. Linear Relationships • Dependent (y) and independent (x) variables when graphed form a straight line • Slope is positive if they are DIRECTLY PROPORTIONAL • Slope is negative if they are INVERSELY PROPORTIONAL

  41. Nonlinear Relationships • Quadratic equations relate parabolic relationships • Some inverse relationships are hyperbolic

  42. Practice Problem • Create a graph from the data chart given • Describe the relationship (linear or non) • If linear, find slope (in/direct)

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