Solve the following problem.
Compare the cost of electricity for two local electric co-ops. Wild Rice Co-op charges 0.094 dollars per kilowatt-hour with a surcharge of 0.008 dollars per kilowatt-hour. Cattail Lake Co-op charges 0.0959 dollars per kilowatt-hour with a surcharge of 0.0052 dollars per kilowatt-hour.
The problem involves the addition of decimals and the comparison of decimals since the total charge per kilowatt-hour needs to be determined for each co-operative before the values are compared. When we make the comparisons, we need to be very careful that we are comparing their place-values and not the number of nonzero digits. For example, if we compare the surcharges, we note the 0.008 (eight thousandths) is more than 0.005 (five thousandths). So, we would conclude that 0.008 > 0.0052. We would not compare the 8 and 52, which would have given us an incorrect solution since 52 > 8.
We note that without the surcharge Wild Rice Co-op has a lower cost per kwh since 0.094 < 0.0959, but the surcharge for Cattail Lake Co-op is less since 0.0052 < 0.008. By adding the charge and surcharge, we find that the cost per kwh for Wild Rice Co-op is 0.102 dollars per kwh and for Cattail Lake Co-op is 0.1011 dollars per kwh. The cost of electricity for Cattail Lake Co-op is less than that of Wild Rice Co-op since 0.1011 < 0.102. If we subtract their costs, we find that the cost for Cattail Lake Co-op is 0.0009 dollars per kwh hour less than that of Wild Rice Co-op.
This problem motivates the importance of place value when comparing decimals. It also motivates the use of place value for lining up the decimal points in the addition and subtraction of decimals.
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Date last modified: June 26, 2010.
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By Kris Montis and Timothy Peil
