Calculating Parts per Million: Do We Have a
Problem Here?
Brink Harrison
Time:
One class period
Preparation
5-10 min copying overheads
Time:
Materials: Number Game Overhead
Instructor's Answer Key
Abstract
Students will use unit analysis to calculate parts per million represented by given ratios and
determine in a given scenario whether local health officials should close a lake that has been
contaminated.
Purpose – Students will be able to calculate ppm and use this number to make decisions
concerning health risks.
Objectives
Students will be able to:i.
Calculate ppm and ppb by using unit analysis when given a ratio of amounts
ii.
Determine in ppm what constitutes a health risk for a particular toxin given data
National Science Education Standard:
Measurement
Understand measurable attributes of objects and the units, systems, and processes of
measurement
Apply appropriate techniques, tools, and formulas to determine measurements
Teacher Background
See attached sheets
Related and Resource Websites
http://www.ucar.edu/learn/1_5_2_24t.htm
http://www.epa.gov/superfund/students/clas_act/haz-ed/numbers.htm
Activity
Have the students present their representations of the concentration of one part per million to the
class. Allow time for discussion of the representations. Make sure that you do the dilution activity
last and pass out the chart from the Dilution Activity to the rest of the class. Complete the chart
with the rest of the class and have the class answer the following questions:
http://pulse.pharmacy.arizona.edu/math/calculating_ppm.html
1. Which containers have the highest concentration? (# 1) The lowest concentration? (# 10)
2. Which container has the highest mixing ratio? (# 1) Which has the lowest mixing ratio?
(# 10)
3. What happens to the color of the liquid as the mixing ratio decreases? (it becomes lighter)
Why does this happen? (The number of dye molecules becomes diluted ten times by water in
each progression of the serial dilution.)
4. Does the liquid ever become colorless? (yes). If so, at what mixing ratios is the liquid
colorless? (Answers will vary depending upon the strength of the initial solution.) Why do you
think it is colorless? (So few dye molecules are present that they are not visible.)
5. Which test tube contains one ppm of coloring? (#7) Which test tube contains one ppb of
coloring? (#10)
6. Ozone in the stratosphere has a mixing ratio in the range of one to ten ppm. Which containers
represent one and ten ppm? (#7 and #6)
7. A typical mixing ratio for ozone in the troposphere is 10 to 100 ppb. Which test tubes represent
this range of mixing ratios? (#8 and #9)
http://www.ucar.edu/learn/1_5_2_24t.htm
Tell the students, “You now should be able to visualize what a concentration of one ppm looks
like. Today we are going to use unit analysis to actually calculate the parts per million
represented by certain ratios.”
The rest of the activity has been adapted from
http://www.epa.gov/superfund/students/clas_act/haz-ed/numbers.htm
Hand out the Student worksheet, The Numbers Game, and have the students take the quiz in
Part A. The quiz is intended to gauge the students' intuitive grasp of how small a “part-per-million”
and a “part-per-billion” are. Instruct the students to guess at the answers of these three questions,
not to do the calculations.
After the students have completed Part A, go to Part B where they will calculate each answer
choice and, from these calculations, determine the correct answer to each question in the quiz.
Finally, work through the Lake Jasmine spill scenario in Part C with the students. An answer key
to the questions is provided in the Teacher Background sheets.
The Numbers Game
Part A
Just how small is a part per million? A part per billion? Answer the following three questions
based on your “gut reaction.” Guess if you need to, do not do the calculations.
One part per million is equivalent to 1 minute in
a. 1 day
b. 2 years
c. 6 weeks
One part per billion is equivalent to 1 second in
a. 3 weeks
b. 17 months
b. 32 years
http://pulse.pharmacy.arizona.edu/math/calculating_ppm.html
Part B
Now go back and calculate each of the answers you chose in Part A. Use the procedure below
for each calculation.
To calculate the relationship between 2 quantities, use unit analysis to set up your equation. For
example, to compare years and seconds, convert one year into seconds. To do this, set up ratios
for days per year, then hours per day, minutes per hour, and finally seconds per minute. The units
will cancel out and you will be left with the number of seconds per year.
 365 days  24 hours  60 min



 1 year  1 day  1 hour
 60 sec  31,536,000 sec

 
1 year
 1 min 
1. Use the space below to calculate the ratios representing (a) 1 minute per day, (b) 1 minute
per 2 years, and (c) 1 minute per 6 weeks. After you have completed each conversion, you
may have to round your answers to the nearest thousand, million or billion to find the correct
answer to the quiz question.
2. Use the space below to calculate (a) 1 second per 3 weeks, (b) 1 second per 17 years, and
(c) 1 second per 32 years to find the answer to question 2.
Part C
If the conversion of units leads to a fraction with a numerator other than 1, a different method can
be used to determine parts per million or parts per billion. Be sure your fraction has a smaller
number on top and larger number on the bottom and divide.
To express the decimal answer in parts per million, move the decimal point 6 places to the right.
To express the answer in parts per billion, move the decimal point 9 places to the right.
Example 1:
20 oz  20 oz  1lb 
20 oz
20

 
 

 .0125
100 lb  100 lb  16 oz  1,600 oz 1,600
Moving the decimal place 6 places to the right gives 1,250 parts per million.
Moving the decimal place 9 places to the right gives 1,250,000 parts per billion.
You would probably not see a number this large expressed in parts per billion. It is better
expressed as a smaller number of parts per million.
Example 2:
 11oz  1ton  1lb 
11oz
11oz
11


 
 

 0.000034375
10 tons  10 tons  2000 lb  16 oz  320,000 oz 320,000
Moving the decimal place 6 places to the right gives 34.37, or about 34.4 parts per million.
Moving the decimal place 9 places to the right gives 34,370, or about 34,000 parts per billion.
http://pulse.pharmacy.arizona.edu/math/calculating_ppm.html
Scenario
Lake Jasmine is a 20-acre lake with an average depth of 30 feet. Yesterday afternoon, four 55gallon drums of Fuel Oil A and six 55-gallon drums of Solvent C fell off a truck during an accident,
rolled into lake Jasmine and burst open on the rocky shore. The entire contents of all the drums
spilled into the lake.
Based on the scenario described below and the table of legally allowable concentrations of
contaminants in surface water, decide whether local public health officials should take
measures to keep campers near Lake Jasmine from using the water.
Allowable Quantities:
(above these levels require
action)
Conversion Table:
Fuel Oil A 2.2 ppm in recreational waters
Solvent C 1.3 ppm in recreational waters
1 acre = 43,560 square feet
1 gallon = 0.1337 cubic feet
1 cubic foot = 7.48 gallons
STEP 1
Calculate the concentration of each contaminant (in ppm) in Lake Jasmine. To do this you must
compare the volume of the contaminants (gallons) to the volume of the lake (cubic feet). Start by
converting both to cubic feet.
Calculate the volume of the lake:
Water in Lake Jasmine:
Calculate volume of contaminants:
Fuel Oil A:
and
Solvent C:
Comparison of amounts:
Fuel Oil A:
Move the decimal point the appropriate number of places to the right to calculate the ppm of Fuel
Oil A
Solvent C:
Move the decimal point the appropriate number of places to the right to calculate the ppm of
Solvent C
http://pulse.pharmacy.arizona.edu/math/calculating_ppm.html
STEP 2
Compare these levels to the values in the chart of allowable quantities to see if they exceed the
legally allowable levels.
Allowable Quantities: (concentrations of contaminants above these levels require action)
Fuel Oil A
2.2 ppm in recreational waters
Solvent C
1.3 ppm in recreational waters
What is your decision about whether or not local public health officials should take measures to
keep vacationers near Lake Jasmine out of the water? Explain your decision.
Homework
The MCL of various toxins is as follows:
Arsenic
MCL: 0.05 mg/L
Benzene
MCL: 0.005 mg/L
Copper
MCL: 1.3 mg/L
Lead
MCL: 0.015 mg/L
Styrene
MCL: 0.1 mg/L
Assuming that you are still at Lake Jasmine, which has a volume of 26,136,000 cubic feet, how
many cubic feet of each of the above toxins could be spilled into the lake before health officials
would need to take action?
Embedded Assessment
Informal discussion as the students present their models of ppm will allow you to assess their
understanding of how small a concentration of one ppm truly is. Informal observations when the
students are using unit analysis to calculate the ppm of a given ratio allows assessment on their
understanding of the procedure they need to follow. Guided practice and informal observations
can be used with the Number Game to assess how well the students use synthesis to combine
the two ideas to come to a decision of what to tell the health officials at Lake Jasmine.
http://pulse.pharmacy.arizona.edu/math/calculating_ppm.html