Compute the check digit c for the following ISBNs a 03167694

Compute the check digit c for the following ISBNs.

a) 031676948 - c

b) 140123517 - c

Please how the answer was computed

Thanks

Solution

a) 031676948 - c

For an ISBN check digit, multiply the first digit by 10, the second digit by 9, the third digit by 8, ..., the ninth digit by 2 and add up all these numbers. The check digit is the number that add to this total to get up to a multiple of 11.

0*10 +3*9 +1*8 +6*7 +7*6 +6*5 +9*4 +4*3 +8*2 =213

next nearest multiple of 11 is 220 which is 7 more than 213

Hence check digit=7

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b) 140123517 - c

1*10 +4*9 +0*8 +1*7 +2*6 +3*5 +5*4 +1*3 +7*2 =117

next nearest multiple of 11 is 121 which is 4 more than 117

Hence check digit=4