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If you weren't convinced that learning to keep units in a calculation was important, here is a little story that might change your mind. This audio clip spread quickly around the web in early 2009. You can listen to the full 27 minute phone conversation here: http://www.videosift.com/video/Verizon-002-dollars-002-cents.

Just in case the clip is no longer available (or if you don't have the patience to put up with listening to 27 minutes of unimaginable frustration), here's the story. A phone company customer had a service plan that provided unlimited data to his web-capable phone. When he was planning a trip to Canada, he knew that when he was out of the country he would be charged for his data link by the number of kilobytes transferred, but he did not know the rate. He called his phone company and was assured that the rate was "0.002 cents per kilobyte." He was surprised it was so small and asked for a confirmation and to have it written explicity in the record of his call. This was done.

He then used the internet freely while in Canada and wound up transferring 35,893 kilobytes. When he received his bill he was charge $71.79. He was convinced that the correct charge was 71.79 ¢

A. Was he correct? Or was the phone company's charge correct? Tell what the correct charge is and how you know.

He then called his phone company and spent 27 minutes on the line with three different supervisors, none of whom he was able to convince that the correct charge was 71.79 ¢. It appears that what appears on the phone company screens as a rate is "0.002" without any units. When the computer calculates, it multiplies by the number of kilobytes used and reports the result in dollars.

But three different phone company agents all read the 0.002 as 0.002 cents. One even insisted that 0.002 cents = 0.002 dollars.

B. Write a letter to the phone company explaining clearly why the correct charge is 71.79 ¢ if the rate is what they quoted -- and in a fashion that would convince someone who would say "0.002 dollars is equal to 0.002 cents because it's less than a dollar" or "well have you ever seen a fraction of a cent?"

Problem by E. F. Redish, H. Dobbins, and K. Hall

Page last modified April 5, 2009: G38