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The Numbers Game - Student Worksheet

The Numbers Game

Student Worksheet

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.

  1. One part per million is equivalent to 1 minute in
    a. 1 day b. 2 years c. 6 weeks

  2. One part per billion is equivalent to 1 second in
    a. 3 weeks b. 17 months b. 32 years

    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, first convert both quantities to the same unit of measure. For example, to compare years to seconds, convert the years to seconds. To do this, convert the years to days, then the days to hours, the hours to minutes, and the minutes to seconds:

365 days   x   24 hours   =   8,760 hours
______ ______ ______
1 year 1 day 1 year

8,760 hours   x   60 minutes   =   525,600 minutes
______ ______ ______
1 year 1 hour 1 year

525,600 minutes   x   60 seconds   =   31,536,000 seconds
______ ______ ______
1 year 1 minute 1 year

After you have completed the conversion to the same units (e.g., expressing hours, days, or weeks in minutes or seconds), you may have to round your answer to the nearest thousand, million, or billion.

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 of Part A.


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 ounces = 2 ounces = 2 ounces = 2 =>  
------ ------ ------ ------
100 pounds (100 x 16 ounces) 1,600 ounces 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:

11 ounces = 11 ounces = 11 ounces = 11 =>  
------ ------ ------ ------
10 tons 20,000 pounds (20,000 x 16) ounces 320,000 ounces

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.

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 vacationers near Lake Jasmine out of the water.

Allowable Quantities: Fuel Oil A 2.2 ppm in recreational waters
(concentrations of contaminants Pesticide B 4.7 ppm in recreational waters
above these levels require action) Solvent C 1.3 ppm in recreational waters


Conversion Table: 1 acre = 43,560 square feet
1 gallon = 0.1337 cubic feet
1 cubic foot = 7.48 gallons


Lake Jasmine is a 20-acre lake with an average depth of 30 feet. Yesterday afternoon, four 55-gallon 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.

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. To calculate the volume of the lake, multiply the area (in square feet) by the depth (in feet) to get cubic feet.

Compare these levels to the values in the chart of allowable quantities to see if they exceed the legally allowable levels.


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