AP Environmental Science Math Review
(remember…..there are NO calculators allowed on the AP exam)
I.
II.
Scientific Notation
a. Writing numbers in scientific notation
b. Operations with scientific notation
Metric System
a. Converting within the Metric System
b. Using dimensional analysis in conversions
Instructions: Read the following information and complete the practice problems.
I.
Scientific Notation
a. Writing numbers in scientific notation
Scientific notation expresses numbers as the product of two numbers: a coefficient (value >1 and
>10) and 10 raised to a power. This is a valuable tool to use when dealing with very large and
also very small numbers.
Examples:
210 is expressed as 2.1 x 102
0.021 is expressed as 2.1 x 10-2
Practice Problems:
Express the following numbers in scientific notation:
a. one billion (1,000,000,000)
b. 0.00000001
c. 345
d. 450
e. 0.00205
f. 65,000
g. 6,500
h. 0.0000054
Write out the following numbers given in scientific notion:
a. 4.67 x 105
b. 2.3 x 10-7
c. 9.345 x 109
d. 1.0 x 10-2
e. 7.93 x 10-5
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b. Operations with scientific notation:
 Multiplication: To multiply numbers expressed in scientific notation, multiply the
coefficients and add the exponents.
Example: (3 x 103) x (4 x 105)
Multiply the coefficients: 3 x 4 = 12
Add the exponents: 3 + 5 = 8
Answer would be: 12 x 108
To follow the rules for scientific notation your final answer would be 1.2 x 109
 Division: To divide numbers expressed in scientific notation, divide the coefficients
(numerator by denominator) and subtract the denominator’s exponent from the
numerator’s exponent.
Example: 5.2 x 104
2.6 x 102
Divide 5.2 by 2.6 = 2
Subtract 2 from 4 = 2
Final answer 2.0 x 102
 Addition and subtraction: If the exponents are different, convert one to match the other
exponent and follow the above rules.
Example:
(2.0 x 104) + (2.3 x 104) = 4.3 x 104
(5.7 x 1012) - (4.1 x 112) = 1.6 x 1012
If the exponents are different, convert one to match the other and follow the above rules.
Example: (4.2 x 102) + (5.3 x 103)
If you increase the power you move the decimal to the left.
Change 4.2 x 102 to 0.42 x 103
If you decrease the power you move the decimal to the right.
Change 5.3 x 103 to 53 x 102
SO: 4.2 x 102
+ 53 x 102
or
.42 x 103
+ 5.3 x 103
Practice Problems: Complete the following calculations:
a. (8.7 x 1018) x (8.7 x 1022)
b. (4.2 x 1012)
(2.1 x 103)
c. Add 3 billion to 14 million (using scientific notation)
d. (5.23 x 105) - (4.22 x 103) =
e. (3.5 x 106) + (2.3 x 10-2) =
2
II.
Metric System
a. Converting within the Metric System
Units of Distance: (base unit is Meter)
1000 m (103) = 1 km
one thousand meters = 1 kilometer
100 cm (102) = 1 m
one hundred centimeters = 1 meter
1000 mm (103) = 1 m
one thousand millimeters = 1 meter
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1000 m (10 ) = 1 mm
one thousand micrometers = 1 millimeter
Units of Mass: (base unit is the gram)
1000 (103) kg = 1 metric ton one thousand kilograms = 1 metric ton
1000 (103) g = 1 kg
one thousand grams = 1 kilogram
1000 (103) mg = 1 g
one thousand milligrams = 1 gram
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1,000,000 (10 ) ng = 1 mg one million nanograms = 1 milligram
Units of Volume: (base unit is the Liter)
1000 L = m3
one thousand Liters = 1 cubic meter
1000 mL = 1 Liter
one thousand milliliters = 1 Liter
b. Using Dimensional Analysis in conversions
You can change from one unit to another by using conversion factors.
Cancel out known units to arrive at units wanted.
Conversion factors are equalities such as 12 eggs = 1 dozen
Conversion factors would be written as
12 eggs
or dozen
Dozen
12 eggs
Example: How many milliliters are in 1.5 Liters?
1.5 Liters x
1000 mL = 1500 mL
1 Liter
Practice Problems: Use dimensional analysis to solve the following problems:
a. How many micrometers are in 4.2 meters?
b. How many kilograms are in 5,000 grams?
c. Measure your weight. Express the measurement in pounds, grams, and kilograms using the
following equalities. Show your work. 1 pound = 454 grams and 1 kilogram = 1000 grams
d. What is the speed of light in miles per hour? Speed of light – 3.0 x 108 meters/second and
1 mile – 1.609 kilometers
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