Download Quantification of Environmental Problems

Quantification of Environmental Problems
In this problem set, we will explore two fundamental components of expressing and quantifying environmental
problems: scientific notation and calculating percentage changes overtimes.
I- SCIENTIFIC NOTATION
Environmental science often deals with very large numbers (e.g., biomass production of a forest) and very small
numbers (contamination of an aquifer). To better manage these data, and to decrease errors, scientists have
developed a shorter method to express numbers using scientific notation. Scientific notation is based on powers of
the base number 10. Thus, for example, an environmental scientist calculates that 146,000,000,000 kilograms of
biomass was produced in a test plot during the previous year. Using scientific notation, the number would be:
1.46 X 1011
To write a number in scientific notation for 146,000,000,000:
Step I: place the decimal after the first digit and drop all the zeroes.
1.46
000,000,000
Step 2: count the number of places from the decimal to the end of the number. For example:
1
.
4
6
0
0
0
0
0
0
0
Count
.
1
2
3
4
5
6
7
8
9
0
0
10
11
There are 11 places after the decimal point; therefore the exponent is 11. Thus 146,000,000,000 becomes
1.46 x 1011.
152,000,000 is 1.52 X 108
Exponents in scientific notation are often expressed in different ways. For example, 146,000,000,000 can also be
written as:
1.46E + 11 or as 1.46 X 10^11
A similar approach is used for small numbers (< 1), which will have a negative exponent. A millionth of a second is:
0.000001 sec. = 1.0 x 10-6 (or 1.0E -6 or 1.0^ -6)
Thus, with small numbers, you count from the decimal the number of zeroes until you reach the first non-zero
number.
0.00000123 sec. = 1.23 X 1O-6
Exercise: Scientific Notation
Convert the following numbers into or; from scientific notation:
1. 678,950,000,000 =_________________
2. 1,000,000,000,000 =_________________
3. .00000004567 =_________________
4. 5,689,000,000 =_________________
5. 8923 =_________________
6. .000000045678963 = _______________
7. 2.223 X 10-9=-_________________
8. 3.19E+ 12 =____________________
9. 4.444^ -4 =__________________
10. 7.47 X 1013 =________________
II- CALCULATING PERCENT CHANGE
Environmental scientists often analyze trends. A popular approach to communicating these trends is percentage
increase/decrease over time. In calculating percentage of change (whether an increase or a decrease), you are
concerned with the difference between two numbers and how much of the first number added to or subtracted from
the first number will produce the second number.
The three steps to calculate a percentage are:
1. Subtract
2. Divide
3. Multiply
Subtract: New number - original number = change
Divide: by original number
Multiply: by 100
Thus, the basic formula is simple:
Percent increases and decreases are calculated with respect to the value before the change took place— the
original number.
A. In 2004, the level of acetone in the river was 100 parts per million (ppm). In 2004, the level increased by 12
ppm. What is the percentage increase in acetone?
12/100 = .12 X 100 = 12%
B. In 2000, the level of ammonia was 63 ppm. In 2004, the level is 112 ppm. What is the percentage of increase
since 2000?
Step 1: Determine the amount of change.
112 -63 = 49
Step 2: Divide the change by the original number, then multiply by 100.
49/63 = .777 X 100 = 77.7%
C. Last month, the level of hexachlorobenzene had decreased by 8 ppm. If the level is now 47 ppm, by what
percentage did the level of hexachlorobenzene decrease? The amount of change is 8, therefore the original amount is
47 + 8 = 55.
8/55 = .145 X 100 = 14.5%
D. A utility's operating costs for its electrostatic precipitator was the following:
2001 = $345,000
2002 = $325,000
2003 = $345,000
What were the annual percentage changes?
2001 to 2002: ($325,000 - $345,000)/$345,000 X 100 = -5.79%
2002 to 2003: ($345,000 - $325,000)/$325,000 X 100 = 6.15%
Exercise: Calculating Percentage Changes
Solve the following.
1. 234.98 to 324.77 =____________% change
2. 324.77 to 234.98 =____________% change
3. 7.14 X 107 to 8.47 X 108 =____________% change
4. 100 increases by 300% =____________
5. 756 declines by 100% =__________ __
6. 756 increases by 100% =____________
7. A utility's total pollution control costs are broken down as follows:
Air pollution control = $234,000
Wastewater treatment = $167,000
Solid waste = $45,000
Hazardous waste = $12,000
What percentage does the company spend for each?
Air pollution control =_________%
Wastewater treatment =________%
Solid waste =_________%
Hazardous waste =__________%
8. The company's managers want to budget sufficient money for next year. Assuming that costs will increase by
2.4%, what will the costs be for next year for each category?
Air pollution control = $_________
Wastewater treatment = $__________
Solid waste = $_________
Hazardous waste = $_________
9. An environmental scientist has the following data on mercury concentrations in small mouth bass (Micropterus
dolomieu) sampled from a pond. What is the annual mean concentration for each year? What is the mean for all
three years?
2002
2003
2004
7.2 X 104
2.1 X 104
6.4 x F104
6.5 x 104
4.1 x 104
7.7 x 104
7.1 X 104
7.0 X 104
5.2 x 104
6.6 x 104
7.3 x 104
7.2 x 104
6.9 x 104
5.9 x 104
7.1 x 104
7.1 x 104
5.0 x 104
9.4 x 104
7.5 x 104
5.1 x 104
2.1 x 104
10. What is the percentage difference between 2002 and 2003 and between 2003 and 2004 based on the annual,
average mercury concentration?
11. Why is it important for a member of an environmentally literate society to be able to understand scientific
notation and percentages?