1. You CAN do math without a calculator!
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 
model to actual 4

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

6. Order of Magnitude Ratio/Relationship-usually base 10 in APES
milli(m) (thousandth)
Base
Kilo(k) ,000 (thousand)
Mega(M) ,000,000 (million)
Giga(G) ,000,000,000 (billion)
Tera(T) ,000,000,000,000 (trillion)
Ratio/Relationship-usually base 10 in APES
So you are probably most familiar with 6

7. 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
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

8. 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

9. 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)

10. 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

11. 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

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

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

14. 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

15. 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 x 107

16. 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?

17. 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 W
0.9x 10-6 W = W
9.0x W = W

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

19. 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 joules = 12 joules + 10 joules joules 19

20. Energy Quality ≠ Energy Quality
ENERGY IN = ENERGY OUT
Energy Quality ≠ Energy Quality
Before Transformation = After Transformation
200 joules = Starting Energy 
100 joules 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

21. The 10% Rule

22. 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

23. 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) joules of light energy
means 95% of what you put in went to light; 5% to heat
d) joules of light energy
e) joules of heat energy

24. 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?

25. 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

26. 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

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

28. 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

29. 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

30. 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

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… 31

32. 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

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

34. 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?

35. 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

36. 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 = kcal
1 Btu = 1055 J = 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) = 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 = J 36