Math Skills for APES Calculations Without Calculators

The Metric Mountain the prefix tells the scale of measurement

Know some basic metric prefixes for simple conversions

GigaG10 9 = MegaM10 6 = Kilok10 3 = Base 10 0 =1 (m, l, g) Centic10 -2 =.01 Millim10 -3 =.001 Micro μ10 -6 = Nano n10 -9 =

Metric Conversions 2.50 x m to Mm 450 g to kg 56 cm to mm All answers must use scientific notation!

Use exponents whenever numbers are especially large or small. Scientific notation is a way to express, numbers the form of exponents as the product of a number (between 1 and 10) and raised to a power of  9.8 x  1.23 x 10 -4

In scientific notation remember to have one number to the left of the decimal and to use correct significant figures.

Scientific Notation 67 million 748 ten-thousandths 3 thousand

Math With Exponents 5.6 x 10 7 x 3.1 x = 244 x10 3 / 1.22 x 10 2 = 12,000 x 30 x 10 9 =

Practice math manipulations with exponents When adding or subtracting numbers with exponents the exponents of each number must be the same before you can do the operation. Example: (1.9 x ) – (1.5 x ) (19 x ) - (1.5 x ) = 17.5 x 10 -4

When multiplying numbers with base 10 exponents, multiply the first factors, and then add the exponents. Example, (3.1 x 10 5 ) (4.5 x 10 5 ) = x or 1.4 x When dividing numbers, the exponents are subtracted, numerator exponent minus denominator exponent. Example: 9 x 10 5 = 3 x x 10 3

Use Dimensional Analysis or factor/label method for calculations Given Value x Conversion factor =Answer 1 OR given unit x new unit = new unit 1 given unit Example: 25 ft x 1 yd x m =~ 9.12 meters 3 ft 1 yd

Be sure to know how to convert numbers to percentages and percent change. Example: If 200 households in a town of have solar power, what percent does this represent? 200/10000 x 100%= ? Example: If a city of population 10,000 experiences 100 births, 40 deaths, 10 immigrants, and 30 emigrants in the course of a year, what is its net annual percentage growth rate?

Conversion Factors will ALWAYS be given 1kWh = 3400 BTU 1 BTU = 1050 J 2.2 = 1 kg 1 mi 2 = 640 acres 1 ha = 10,000 m 2 = 2.47 acres 1 metric ton = 2,205 lbs = 1,000 kg

Show ALL of your work and steps of calculations, even if they are too simple.

Percent Change An unknown article states that NOx emissions have increased from 25 Gt to 130Gt annually. What is the percent change in NOx emissions?

Show all of your units, too! Numbers given without units are often not counted even if correct.

Answers should make sense! LOOK them over before you finish Example: No one is going to spend 1 billion dollars per gallon of water!

Keep it simple. They don’t expect you to do calculus! Try reducing the fraction from the previous problem 200/1000 to 2/10= 1/5 Then solve: 1/5 x 100%= 20%

Doubling Time Rule of 70: t = 70/r% Example: A country with a population of 800 million has a growth rate of 4% in In what year will the population double?

Be able to calculate half life Example: A sample of radioactive waste has a half- life of 10 years and an activity level of 2 curies. After how many years will the activity level of this sample be 0.25 curie?

Know how to graph data Title the graph Set up the independent variable along the X axis Set up the dependent variable along the Y axis Label each axis and give the appropriate units Make proportional increments along each axis so the graph is spread out over the entire graph area Plot points and sketch a curve if needed. Use a straight edge to connect points unless told to extrapolate a line Label EACH curve if more than one is plotted.

Know what is meant by “per capita” when solving a problem or interpreting a graph

Be able to interpolate and extrapolate data

Remember that the numbers will likely be simple to manipulate. If you are getting answers like 1.365, then it is likely wrong