<P> For example, the ISBN - 13 check digit of 978 - 0 - 306 - 40615 -? is calculated as follows: </P> <P> Thus, the check digit is 7, and the complete sequence is ISBN 978 - 0 - 306 - 40615 - 7 . </P> <P> In general, the ISBN - 13 check digit is calculated as follows . </P> <Dl> <Dd> r = (10 − (x 1 + 3 x 2 + x 3 + 3 x 4 + ⋯ + x 11 + 3 x 12) mod 10). (\ displaystyle r = (\ big () 10 - (\ big () x_ (1) + 3x_ (2) + x_ (3) + 3x_ (4) + \ cdots + x_ (11) + 3x_ (12) (\ big)) \, (\ bmod (\,)) 10 (\ big)).) </Dd> </Dl>

What is the meaning of isbn in library