You CAN do math without a calculator! 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  model to actual http://www.powersof10.com/film 4

King Henry Doesn’t Usually Drink Chocolate Milk!

Order of Magnitude Ratio/Relationship-usually base 10 in APES 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 So you are probably most familiar with 6

Prefix Symbol Power Factor yotta Y 1024 1,000,000,000,000,000,000,000,000 zetta Z 1021 1,000,000,000,000,000,000,000 exa E 1018 1,000,000,000,000,000,000 peta P 1015 1,000,000,000,000,000 tera T 1012 1,000,000,000,000 giga G 109 1,000,000,000 mega M 106 1,000,000 kilo k 103 1,000 hecto h 102 100 deka da 101 10 deci d 10-1 0.1 centi c 10-2 0.01 milli m 10-3 0.001 micro µ 10-6 0.000,001 nano n 10-9 0.000,000,001 pico p 10-12 0,000,000,000,001 femto f 10-15 0.000,000,000,000,001 atto a 10-18 0.000,000,000,000,000,001 zepto z 10-21 0.000,000,000,000,000,000,001 yocto y 10-24 0.000,000,000,000,000,000,000,001

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

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)

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 6.1 x 1.35 = 6.1 x 109 1% 2% 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

Scientific Notation Or 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

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

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

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

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?

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

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

It’s the Law! The Law of Conservation of Energy Energy is NEVER created or destroyed ONLY TRANSFORMED Everytime we transform it, some of it becomes unusable to us, but it is still energy Mathematically what does that mean? 200 joules = 100 joules + 100 joules = 12 joules + 10 joules + 178 joules 19

Energy Quality ≠ Energy Quality ENERGY IN = ENERGY OUT Energy Quality ≠ Energy Quality Before Transformation = After Transformation 200 joules = Starting Energy  100 joules + 100 joules = chemical energy + heat energy Remind the students that since energy cannot be created nor destroyed, 100% of the energy that is put into a system exits that system. Of all the sun’s energy that enters the biosphere, ALL of it eventually exits. 20

The 10% Rule

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

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

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?

Half-life 1 -½ ½-¼ ¼-⅛ 1/8- 1/16 How many half lives? 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

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

HALF LIFE RELATIONSHIPS Percentage Decimal Fraction 100% 1.00 1/1 1 50% .50 ½ 2 25% .25 ¼ 3 12.5% .125 1/8 4 6.25% .0625 1/16 5 3.125% .03125 1/32 6 1.563% .01563 1/64

Burning fossil fuels Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O Burning of Natural Gas (Methane) CH4 + O2 CO2 + H2O Balance these equations to see the difference in CO2 production with octane (gasoline--top equation) and methane (natural gas--bottom equation) Note that 16 times MORE carbon dioxide is produced for every molecule of octane burned… 28

Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O C C H H O O Burning fossil fuels Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O C C H H O O Balance these equations to see the difference in CO2 production with octane (gasoline--top equation) and methane (natural gas--bottom equation) Note that 16 times MORE carbon dioxide is produced for every molecule of octane burned… 29

Burning fossil fuels Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O C 16 C 16 H 36 H 36 O 50 O 32+18=50 2 25 16 18 Balance these equations to see the difference in CO2 production with octane (gasoline--top equation) and methane (natural gas--bottom equation) Note that 16 times MORE carbon dioxide is produced for every molecule of octane burned… 30

Burning fossil fuels Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O Burning of Natural Gas (Methane) CH4 + O2 CO2 + H2O 2 25 16 18 Balance these equations to see the difference in CO2 production with octane (gasoline--top equation) and methane (natural gas--bottom equation) Note that 16 times MORE carbon dioxide is produced for every molecule of octane burned… 31

Burning fossil fuels Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O Burning of Natural Gas (Methane) CH4 + O2 CO2 + H2O 2 25 16 18 Balance these equations to see the difference in CO2 production with octane (gasoline--top equation) and methane (natural gas--bottom equation) Note that 16 times MORE carbon dioxide is produced for every molecule of octane burned… 2 2 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?

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?

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 7.96 bkWh/12= 0.66 bkWh per month

Energy Units Btu (British thermal unit) – cal (calorie) or kilocalorie (kcal) J (joule) W (watt) Hp (horsepower) Q (Quad) Students might want to jot down these units and their equivalents. They are likely to encounter them on the APES exam. the derived unit of energy in the International System of Units. Joule is equal to 1 watt-second. 1 Btu = 252 cal = 0.252 kcal 1 Btu = 1055 J = 1.055 kJ; 1 Q = 1015 BtuTwo other units that are often seen are the horsepower and the watt. These are not units of energy, but are units of power. 1 watt (W) = 3.412 Btu / hour 1 horsepower (hp) = 746 W Watt-hour - Another unit of energy used only to describe electrical energy. Usually we use kilowatt-hour (kW-h) since it is larger. 1kW-h = 3.16 megajoules quad (Q) - used for describing very large quantities of energy. 1 cal = 4.184 J www.lander.edu/rlayland/Chem%20103/chap_12.ppt 36