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Uncertainty in Addition and Subtraction

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Rounding Up or Down?
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Rounding Up or Down?


Credit: Tax Credits
Source: http://www.flickr.com/photos/76657755@N04/8125994718/
License: CC BY-NC 3.0

Interest owed on a loan or interest paid on deposits in a bank does not come out as a nice number exactly equal to a set number of dollars and cents.  Invariably there will be a few one-hundredths of a penny over or under. Rounding up or down will follow the usual rule: 0.4 or below rounds down, while 0.5 and above rounds up. So, an account with a total of $43.142 will report it as $43.14 and an account of $43.147 will be $43.15.

News You Can Use

  • Rounding rules work best with data, not with real money. Different techniques will give slightly different end results. For most of us, the difference does not matter. A couple of pennies one way or the other is not very significant. But if rounding is done to a large number of accounts, real money can become involved.
  • “Salami slicing” is not just a butcher’s technique, it is also a type of fraud. The scheme involves somehow manipulating large numbers of transaction in such a way that the individual consumer does not notice the fraud, but the cumulative effect can be profitable. There is no clear information as to the extent of this fraud or whether it has actually ever been attempted.
  • Credit: Sun Wayne
    Source: http://www.flickr.com/photos/28415940@N07/3681264717/
    License: CC BY-NC 3.0

    With internet banking, no physical money is actually transferred. This makes transfers faster and easier, but it also creates opportunities for fraud [Figure2]


  • For example, if a specific transaction results in a final deposit of $210.1345, the number would be rounded down to $210.13 and the extra $0.0045 would be deposited in a separate account controlled by the person manipulating the system. The customer would not notice anything, but if the process is multiplied enough times (as would be the case in a bank with a large number of customers), a significant amount of money can be stolen. This scam has been the basis for a number of movies and TV programs over the years.
  • Watch a video dealing with computer glitches at a bank: https://www.youtube.com/watch?v=eaQTAwLd_ow

Show What You Know

Use the links below to learn more about rounding numbers. Then answer the following questions.

  1. Round off 24.598 to the nearest 0.01.
  2. Round off 97.33 to the nearest 0.1.
  3. What is “bankers rounding”?

Image Attributions

  1. [1]^ Credit: Tax Credits; Source: http://www.flickr.com/photos/76657755@N04/8125994718/; License: CC BY-NC 3.0
  2. [2]^ Credit: Sun Wayne; Source: http://www.flickr.com/photos/28415940@N07/3681264717/; License: CC BY-NC 3.0


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