Casting Out Nines

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Casting out nines is a test to ensure that hand computations of sums, differences, products, and quotients of integers are correct. By looking at the digital roots of the inputs and outputs, the casting-out-nines method can help one check arithmetic calculations. The method is so simple that most schoolchildren can apply it without understanding its mathematical underpinnings.

While extremely useful, casting out nines does not "catch" all errors made while doing calculations. For example, 5x7 = 8. By the casting-out-nines method, it would appear that this multiplication is correct, which it is not. This would also happen with the result of 17, 26, et al. In other words there will be an "uncaught" mistake every nine numbers, this would yield a 90% effectiveness to the method.

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