Calculating the Last Digit of an ISBN NumberDate: 07/15/98 at 09:28:36 From: Daymon Smith Subject: How to Calculate the last number in an ISBN number How do you calculate the last number in an ISBN number? Date: 08/01/98 at 13:44:21 From: Doctor Roberta Subject: Re: How to Calculate the last number in an ISBN number Hi, Daymon - ISBN numbers are created so that the first nine digits are information digits and the last digit, the one you want to calculate, is a check digit. This last number helps people notice and correct mistakes that might be made in recording the information digits. Here is an ISBN number: 0-205-12669-3. The digit 0 indicates the book is written for English-speaking people. The number 205 and the number 12669 identify the publisher and the book published by that publisher. The last digit, the 3, was chosen in the following way. Each digit is given a weight by using the digits 1 to 10 and counting right to left. These weights are added. The sum is: 0(10)+ 2(9)+ 0(8) + 5(7) + 1(6) + 2(5) + 6(4) + 6(3) + 9(2) + __(1) (The digits of the ISBN information numbers are listed in order left to right and weighted by counting down from 10 to 1.) The check digit is chosen to be a number from 0 to 10 so that this weighted sum is a multiple of 11. That is, the sum must be divisible by 11. Let us see what sum we have so far with these particular nine information digits: 0(10)+ 2(9)+ 0(8) + 5(7) + 1(6) + 2(5) + 6(4) + 6(3) + 9(2) = 0 + 18 + 0 + 35 + 6 + 10 + 24 + 18 + 18 = 129 The check digit 3 was chosen because 129 + 3(1) = 132 and 132 is a multiple of 11. 129 is greater than 11(11) = 121 and 14 less than 11(13) = 143. The only possible number from 0 to 10 to use as a check digit is 3. Sometimes the only choice for a check number will be 10. Since this is a two digit number and cannot be used as such, the Roman numeral 10, the symbol X, is used. This system for assigning the last number of an ISBN number makes it possible to detect errors made by writing a single digit incorrectly or by writing a pair of digits in the wrong order. Codes provide some interesting mathematics! - Doctor Roberta, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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