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APES Math You CAN do math without a calculator!

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Types of Calculation Percent Change RateConversionsHalf-life Laws/ Rules

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

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

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King Henry Doesnt Usually Drink Chocolate Milk!

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Order of Magnitude milli(m) 10 -3 0.001 (thousandth) Base 10 0 1. 0 Kilo(k) 10 3 1,000 (thousand) Mega(M) 10 6 1,000,000 (million) Giga(G) 10 9 1,000,000,000 (billion) Tera(T) 10 12 1,000,000,000,000 (trillion) Ratio/Relationship-usually base 10 in APES

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PrefixSymbolPowerFactor yottaY10 24 1,000,000,000,000,000,000,000,000 zettaZ10 21 1,000,000,000,000,000,000,000 exaE10 18 1,000,000,000,000,000,000 petaP10 15 1,000,000,000,000,000 teraT10 12 1,000,000,000,000 gigaG10 9 1,000,000,000 megaM10 6 1,000,000 kilok10 3 1,000 hectoh10 2 100 dekada10 1 10 decid10 -1 0.1 centic10 -2 0.01 millim10 -3 0.001 micro10 -6 0.000,001 nanon10 -9 0.000,000,001 picop10 -12 0,000,000,000,001 femtof10 -15 0.000,000,000,000,001 attoa10 -18 0.000,000,000,000,000,001 zeptoz10 -21 0.000,000,000,000,000,000,001 yoctoy10 -24 0.000,000,000,000,000,000,000,001

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Scientific Notation Patterns 3.0 x 10 3 Moving decimal to the left 0.3 x 10 4 0.03 x 10 5 Moving decimal to the right 30 x 10 2 300 x 10 1

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Finding a Relationship 1% of 100 (10 2 ) is 1 (10 0 ) 1% of 1000 (10 3 ) is 10 (10 1 ) 1% of 1,000,000 (10 6 ) is 10,000 (10 4 ) 1% of 1,000,000,000 (10 9 ) is 10,000,000 (10 7 )

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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? A.8 x10 5 B.8 x10 6 C.8 x10 7 D.8 x10 8 E.8 x10 9

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Answer & Rationale 6.1 x 10 9 = 6,100,000,000 1% 6.1 x 10 7 or 61,000,000 2% 12.2 x 10 7 or 122,000,000 So the answer is somewhere between 6.1 x 10 7 and 12.2 x 10 7

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Scientific Notation Adding & Subtracting (your indices must be the same) Solve: 2.0 x 10 3 + 1.4 x 10 4 = Solve: 2.0 x 10 3 + 1.4 x 10 4 =Options: A. 2.0 x 10 3 + 14 x 10 3 = 16 x 10 3 = 1.6 x 10 4 Or Or B. 0.20 x 10 4 + 1.4 x 10 4 = 1.6 x 10 4

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Scientific Notation Solve: 2.0 x 10 4 - 2.0 x 10 3 Options: A. 20 x 10 3 - 2.0 x 10 3 = -18 x 10 3 = 1.8 x 10 4 B. 2.0 x 10 4 -.2 x 10 4 = 1.8 x 10 4

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Multiplying : multiply the numbers and add exponents of the power of 10 Example: 1.2 x 10 7 x 1.0 x 10 9 = 1.2 x 10 16 Scientific Notation

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Dividing: Divide the numbers and subtract the exponents of the power of 10 Example: 1.2 x 10 16 1.2 x 10 7 = 1.0 x 10 9 Can also be written 1.2 x 10 16 = 1.0 x 10 9 1.2 x 10 7 1.2 x 10 7 Scientific Notation

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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 In Context

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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 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 1.5 x 0.6 = 0.9x 10 -6 W or 9.0x 10 -7 W 0.9x 10 -6 W =.0000009 W 0.9x 10 -6 W =.0000009 W 9.0x 10 -7 W =.0000009 W 9.0x 10 -7 W =.0000009 W

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

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

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

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The 10% Rule

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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

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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

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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?

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Half-life 1 - -- 1/8- 1/16 How many half lives? 200 million 4 (number of half-lives)= 50 million yrs

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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 - -- 120 million 3 (number of half-lives)= 40 million years

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HALF LIFE RELATIONSHIPS Half-LifePercentageDecimalFraction 0 100% 100%1.001/1 1 50% 50%.50 2 25% 25%.25 3 12.5% 12.5%.125.1251/8 4 6.25% 6.25%.0625.06251/16 5 3.125% 3.125%.03125.031251/32 6 1.563% 1.563%.01563.015631/64

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Burning of Gasoline (Octane) C 8 H 18 + O 2 CO 2 + H 2 O Burning of Natural Gas (Methane) CH 4 + O 2 CO 2 + H 2 O Burning fossil fuels

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

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Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O C 16 C 16 H 36 H 36 H 36 H 36 O 50 O 32+18=50 Burning fossil fuels 25 2 1618

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Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O Burning of Natural Gas (Methane) CH4 + O2 CO2 + H2O Burning fossil fuels 25 2 1618

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Burning of Gasoline (Octane) C8H18 + O2 CO2 + H2O Burning of Natural Gas (Methane) CH4 + O2 CO2 + H2O Burning fossil fuels 25 2 1618 2 2

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

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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?

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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 796 bkWh/100 = 7.96 bkWh per year EACH PLANT AVERAGES: 7.96 bkWh/12= 0.66 bkWh per month 7.96 bkWh/12= 0.66 bkWh per month

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Energy Units 1. Btu (British thermal unit) 2. cal (calorie) or kilocalorie (kcal) 3. J (joule) 4. W (watt) 5. Hp (horsepower) 6. Q (Quad) www.lander.edu/rlayland/Chem%20103/chap_12.ppt

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