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Luhn algorithm. The Luhn algorithm or Luhn formula, also known as the " modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers. It is described in US patent 2950048A, granted on 23 August 1960. [ 1]
Numerical digit. The ten digits of the Arabic numerals, in order of value. A numerical digit (often shortened to just digit) or numeral is a single symbol used alone (such as "1") or in combinations (such as "15"), to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits ( Latin digiti ...
Digit sums and digital roots can be used for quick divisibility tests: a natural number is divisible by 3 or 9 if and only if its digit sum (or digital root) is divisible by 3 or 9, respectively. For divisibility by 9, this test is called the rule of nines and is the basis of the casting out nines technique for checking calculations.
Each of the first nine digits of the 10-digit ISBN—excluding the check digit itself—is multiplied by its (integer) weight, descending from 10 to 2, and the sum of these nine products found. The value of the check digit is simply the one number between 0 and 10 which, when added to this sum, means the total is a multiple of 11.
The twelve-point system differs from the above only in using the grade A+, to which the value 12.0 is applied. The 1-2-3-4 system Some school districts use a 1-2-3-4 rating system for grades at the elementary (K–5) level, notably many California school districts including The Los Angeles Unified School District (LAUSD) which switched with the ...
The distribution of the n-th digit, as n increases, rapidly approaches a uniform distribution with 10% for each of the ten digits, as shown below. [70] Four digits is often enough to assume a uniform distribution of 10% as "0" appears 10.0176% of the time in the fourth digit, while "9" appears 9.9824% of the time.
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