EXAMPLE 4 ISBN-10 Single-Error Detection

To illustrate with a specific example why the ISBN-10 method detects single errors, let's say the valid ISBN 1-4292-0900-3 is mistaken as 1-2292-0900-3 (an error in position 2). Because the correct second digit in the weighted sum contributes to the total of 176 and the incorrect second digit contributes , we see that the weighted sum of the incorrect number is . But 158 is not evenly divisible by 11, so the error is detected.