| 释义 |
casting out nines A way of checking the plausibility of arithmetic calculations. The sum of the digits of a product equals the product of the sum of the digits of the numbers multiplied. This is because 10n is 1 modulo 9 for all n. In all cases the summing of digits is repeated until a single digit (i.e. between 0 and 9) is obtained, called the digital root. 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. The name arises as any 9s can be omitted, or cast out, in the process of finding the digital root.
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