Arithmetic procedure of verifying operations using modulo characteristics of digit 9
Casting out nines is any of three arithmetical procedures:[1]
Adding the decimal digits of a positive whole number, while optionally ignoring any 9s or digits which sum to a multiple of 9. The result of this procedure is a number which is smaller than the original whenever the original has more than one digit, leaves the same remainder as the original after division by nine, and may be obtained from the original by subtracting a multiple of 9 from it. The name of the procedure derives from this latter property.
Repeated application of this procedure to the results obtained from previous applications until a single-digit number is obtained. This single-digit number is called the "digital root" of the original. If a number is divisible by 9, its digital root is 9. Otherwise, its digital root is the remainder it leaves after being divided by 9.
A sanity test in which the above-mentioned procedures are used to check for errors in arithmetical calculations. The test is carried out by applying the same sequence of arithmetical operations to the digital roots of the operands as are applied to the operands themselves. If no mistakes are made in the calculations, the digital roots of the two resultants will be the same. If they are different, therefore, one or more mistakes must have been made in the calculations.
Castingoutnines is any of three arithmetical procedures: Adding the decimal digits of a positive whole number, while optionally ignoring any 9s or digits...
of the result, and so on until a single-digit number is obtained. Castingoutnines is a procedure for checking arithmetic done by hand. To describe it...
divisibility by 9, this test is called the rule of nines and is the basis of the castingoutnines technique for checking calculations. Digit sums are...
equation negligible. Thus, one can drop + b 2 {\displaystyle {}+b^{2}\,} out and rearrange the equation to b ≃ a 2 − x 2 a {\displaystyle b\simeq {\frac...
the first cluster of two semiprimes (9, 10), preceding (14, 15). Castingoutnines is a quick way of testing the calculations of sums, differences, products...
equivalent, and C-sharp is considered the same as D-flat). The method of castingoutnines offers a quick check of decimal arithmetic computations performed...
the sum of its senary digits is divisible by 5 (the equivalent of castingoutnines in decimal). If a number is divisible by 6, then the final digit of...
subprocesses." Reducing complexity is also the express purpose of castingoutnines in mathematics. Substitutability and recombinability are closely related...
Avicenna (c. 980–1037) contributed to mathematical techniques such as castingoutnines. Thābit ibn Qurra (835–901) calculated the solution to a chessboard...
and their connections to positional notation, including the use of castingoutnines to determine divisibility by nine. In Chapter e {\displaystyle e}...
opposite Ryan Reynolds in the science fantasy psychological thriller The Nines, written and directed by John August. She later starred in the independent...
Nylon noting that it captures the film's style; "Sennott dressed to the nines in Jewish deli couture is nothing short of pure camp." A second, red band...
the Nines - Uniform Database". exhibits.baseballhalloffame.org. Retrieved December 16, 2017. "National Baseball Hall of Fame - Dressed to the Nines - Uniform...
the former had previously directed an experimental short film "When the Nines Roll Over". "Walk of Punishment" introduces the Tully family at Riverrun...
2019-06-15 Fremont, Maggie (2019-02-09). "Schitt's Creek Recap: Dressed to the Nines in Choking Hazards". www.vulture.com. Archived from the original on 2019-07-01...
based on the book by John Grisham. She was originally hired to work on casting, but asked Schumacher if she could audition for a part. Other film credits...
2021). "EXCLUSIVE — 10 Delays MasterChef Australia Launch To Accommodate Nines Married at First Sight Final Week". TV Blackbox. Retrieved 19 March 2021...
perfect wife and mother of five who also practiced law and dressed to the nines." Jezebel's Hillary Crosley Coker hailed Clair as a "career-driven matriarch...
Too Small and five other stories ’’Wizadora - Sixes And Nines’’ (18 August 1995) Sixes and Nines and five other stories ’’Wizadora - Bubble Trouble’’ (18...
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