casting out nines

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A way of checking the plausibility of arithmetical calculations. The sum of the digits of a sum or product equals the sum or product of the sum of the digits of the numbers used. In all cases the summing of digits is repeated until a single digit (i.e. between 0 and 9) is obtained. For example, 347 has a sum of digits of 14, then 5. Also, 514 has a sum of digits 10, then 1. Then 347 × 514=178 358 with a sum of digits of 32, reducing to 5 which is 5 × 1. However, since 178 349 (and many other numbers) also have a sum of digits which reduce to 5, this method will pick up many, but not all, errors and so does not prove a result is correct.

Subjects: Mathematics.

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