How does an ISBN check digit work, and what kind of error is it designed to catch?

Question

Accepted Answer

Each digit is multiplied by an alternating 1-3-1-3… weight, the products are summed, and the final check digit is whatever value rounds that sum up to the next multiple of 10.
For a 13-digit ISBN: positions are weighted 1, 3, 1, 3, …, all weighted digits are added, and the 13th (check) digit is chosen so the total is divisible by 10.
What it catches: single wrong digits and most transposed (swapped) digits — exactly the typos a human makes typing a number. If the recomputed sum isn't a clean multiple of 10, the number is invalid.
What it does NOT do: it offers no protection against a deliberate attacker, who can just recompute a valid check digit. It's an error-detection code, not a security mechanism.
Tip: Checksums (ISBN, IBAN, credit-card Luhn, CRC) all share this DNA: cheap, catch accidental errors, useless against malice.