The Numbers Game  Student Worksheet

a. 1 day  b. 2 years  c. 6 weeks 
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 
SCENARIO
Lake Jasmine is a 20acre lake with an average depth of 30 feet. Yesterday afternoon, four 55gallon drums of Fuel Oil A and six 55gallon 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.
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. To calculate the volume of the lake, multiply the area (in square feet) by the depth (in feet) to get cubic feet.
STEP 2
Compare these levels to the values in the chart of allowable quantities
to see if they exceed the legally allowable levels.