1 / 38

APES Math

APES Math. You CAN do math without a calculator!. Types of Calculation. Percent Change Rate Conversions Half-life Laws/ Rules. Types of Math Skill. Order of magnitude Scientific notation Scale Metric Language Long Division Estimating Converting to fractions & decimals. Scale. .

carnig
Télécharger la présentation

APES Math

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. APES Math You CAN do math without a calculator!

  2. Types of Calculation • Percent Change • Rate • Conversions • Half-life • Laws/ Rules

  3. Types of Math Skill • Order of magnitude • Scientific notation • Scale • Metric Language • Long Division • Estimating • Converting to fractions & decimals

  4. Scale  http://www.powersof10.com/film

  5. King Henry Doesn’t Usually Drink Chocolate Milk!

  6. Order of Magnitude milli(m) 10-3 0.001 (thousandth) Base 100 1. 0 Kilo(k) 103 1,000 (thousand) Mega(M) 106 1,000,000 (million) Giga(G) 109 1,000,000,000 (billion) Tera(T) 1012 1,000,000,000,000 (trillion) Ratio/Relationship-usually base 10 in APES

  7. Scientific Notation Patterns 3.0 x 103 Moving decimal to the left 0.3 x 104 0.03 x 105 Moving decimal to the right 30 x 102 300 x 101

  8. Finding a Relationship 1% of 100 (102) is 1 (100) 1% of 1000 (103) is 10 (101) 1% of 1,000,000 (106) is 10,000 (104) 1% of 1,000,000,000 (109) is 10,000,000 (107)

  9. Calculations The current global human population is about 6.1 billion and is growing at an annual rate of 1.35 %. If the world population were to grow at this rate for the next year, approximately how many people would be added? • 8 x105 • 8 x106 • 8 x107 • 8 x108 • 8 x109

  10. Answer & Rationale 6.1 x 109 = 6,100,000,000 1% 6.1 x 107 or 61,000,000 2% 12.2 x 107 or 122,000,000 So the answer is somewhere between 6.1 x 107 and 12.2 x 107

  11. Scientific Notation Adding & Subtracting (your indices must be the same) Solve: 2.0 x 103 + 1.4 x 104 = Options: A. 2.0 x 103 + 14 x 103 = 16 x 103= 1.6 x 104 Or B. 0.20 x 104 + 1.4 x 104 = 1.6 x 104

  12. Scientific Notation Solve: 2.0 x 104 - 2.0 x 103 Options: A. 20 x 103- 2.0 x 103 = -18 x 103= 1.8 x 104 B. 2.0 x 104 - .2 x 104= 1.8 x 104

  13. Scientific Notation Multiplying : multiply the numbers and add exponents of the power of 10 Example: 1.2 x 107 x 1.0 x 109 = 1.2 x 1016

  14. Scientific Notation Dividing: Divide the numbers and subtract the exponents of the power of 10 Example: 1.2 x 1016 ÷ 1.2 x 107 = 1.0 x 109 Can also be written 1.2 x 1016= 1.0 x 109 1.2 x 107

  15. Practice In Context The formula for power is voltage times current. A volt*amp is called a Watt (a common unit used for power). P= V x I V=voltage (volts) I=current (amps) Using a multi-meter, you measure the voltage of a solar cell to be 1.5 millivolts and the current to be 0.6 milliamps. What is the power of this solar cell?

  16. Practice Using a multi-meter, you measure the voltage of a solar cell to be 1.5 millivolts and the current to be 0.6 milliamps. What is the power of this solar cell? Power = 1.5 x10-3 v * 0.6 x 10-3 amps 1.5 x 0.6 = 0.9x 10-6 W or 9.0x 10-7 W 0.9x 10-6 W = .0000009 W 9.0x 10-7 W = .0000009 W

  17. Clarification 1.5 millivolts = .0015 0.6 milliamps= .0006 milli= 10-3 or 10 e-3 kilo= 103 or 103

  18. It’s the Law! The Law of Conservation of Energy Energy is NEVER created or destroyed ONLY TRANSFORMED Mathematically what does that mean? 200 joules = 100 joules + 100 joules = 12 joules + 10 joules + 178 joules

  19. ENERGY IN = ENERGY OUT Energy Quality ≠ Energy Quality Before Transformation = After Transformation 200 joules = Starting Energy  100 joules + 100 joules = chemical energy + heat energy 

  20. The 10% Rule

  21. Calculations If an incandescent light bulb used in a house lamp has an efficiency rating of 5%, then for every 1.00 joule of electrical energy consumed by the bulb, which of the following is produced? a) 1.05 joules of energy b) 1.05 joules of heat energy c) 0.95 joules of light energy d) 0.05 joules of light energy e) 0.05 joules of heat energy

  22. Explanation a) 1.05 joules of energy b) 1.05 joules of heat energy cannot be greater than what was put in (1.0 joule) c) 0.95 joules of light energy means 95% of what you put in went to light; 5% to heat d) 0.05 joules of light energy e) 0.05 joules of heat energy means 95% of what you put in went to light; 5% to heat

  23. Other Calculations After 200 million years, only 1/16 of the original amount of a particular radioactive waste will remain. The half-life of this radioactive waste is how many million years?

  24. Half-life After 200 million years, only 1/16 of the original amount of a particular radioactive waste will remain. The half-life of this radioactive waste is how many million years? 1 -½ ½-¼ ¼-⅛ 1/8- 1/16 How many half lives? 200 million ÷ 4 (number of half-lives)= 50 million yrs

  25. Half-life After 120 million years, only 1/8 of the original amount of a particular radioactive waste will remain. The half-life of this radioactive waste is how many million years? 1 -½ ½-¼ ¼-⅛ 120 million ÷ 3 (number of half-lives)= 40 million years

  26. HALF LIFE RELATIONSHIPS

  27. Burning fossil fuels Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O Burning of Natural Gas (Methane) CH4 + O2 CO2 + H2O

  28. Burning fossil fuels Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O C C H H O O

  29. Burning fossil fuels 2 25 16 18 Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O C 16 C 16 H 36 H 36 O 50 O 32+18=50

  30. Burning fossil fuels 2 25 16 18 Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O Burning of Natural Gas (Methane) CH4 + O2 CO2 + H2O

  31. Burning fossil fuels 2 25 16 18 2 2 Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O Burning of Natural Gas (Methane) CH4 + O2 CO2 + H2O

  32. Calculations Biomass provides the nation with 3.28 quads of energy. How many quads of biomass energy are provided by wood and wood waste?

  33. WHEN WORDS ARE NUMBERS When Uranium atoms split, they give off heat. This heat produces high pressure steam that is used to turn a turbine in a nuclear power plant. Each year, the nations 100 nuclear power plants generate 796 bkWh of electricity-roughly 20% of the total US electricity production. How much electricity does the average US nuclear power plant generate each month?

  34. WHEN WORDS ARE NUMBERS Each year, the nations 100 nuclear power plants generate 796 bkWh of electricity-roughly 20% of the total US electricity production. How much electricity does the average US nuclear power plant generate each month? EACH PLANT AVERAGES: 796 bkWh/100 = 7.96 bkWh per year EACH PLANT AVERAGES: 7.96 bkWh/12= 0.66 bkWh per month

  35. Energy Units Btu (British thermal unit) – cal (calorie) or kilocalorie (kcal) J (joule) W (watt) Hp (horsepower) Q (Quad) www.lander.edu/rlayland/Chem%20103/chap_12.ppt

More Related