This is what I don’t understand…

[cruz33]

This is what I don’t understand…

The problem:

Determine the ISBN-13 check digitfor the number 978-0-547-16509
The solution:

Because 9 + 3⋅7 +8 + 3⋅0 + 5 + 3⋅ 4 + 7 + 3⋅1+ 6 + 3⋅5 + 0 + 3⋅9 = 113, the check digit must be 7 to so theweighted sum with the check digits ends in zero.

My calculations:

9x 1 = 9
7 x 3 = 21
8 x 1 = 8
0 x 3 = 0
5 x 1 = 5
4 x 3 = 12
7 x 1 = 7
1 x 3 = 3
6 x 1 = 6
5 x 3 =15
0 x 1 = 0
9 x 3 = 27

9 +21+8+0+5+12+7+3+6+15+0+27 = 113

This is what I don’t understand…

My result is 113, as you can see, that number does not endwith 0.
How do I get it to end in 0?
Can somebody please explain to methe process used in this problem?

Here is a link that I read aboutthis topic...
http://www.uu.edu/dept/math/SeniorPapers/01-02/Oldham.pdf

 

[cruz33]

thanks, just one more question..

You correctly ended with 113.

Now you add a number (which will be the check digit) to 113
such that you end up with 120 (next multiple of 10):
113 + 7 = 120 ; got it?

If instead you ended up with 110, then check digit = 0 ; got that?

Ok, but why I wouldn't round it to 110? Why I have to add 7 instead of subtracting 3 and making it 110 which also ends up with a 0? Just trying to understand the "why" of these mathematical concepts...thank you!

 

[JeffM]

Ok, but why I wouldn't round it to 110? Why I have to add 7 instead of subtracting 3 and making it 110 which also ends up with a 0? Just trying to understand the "why" of these mathematical concepts...thank you!

You are not rounding, which is an approximation that usually creates a small error. You are trying to catch errors, not create them.

A check digit algorithm is an undeviating rule that is designed to catch a high percentage of errors. This one says to add always, not to add sometimes and to subtract sometimes. The add sometimes and subtract sometimes rule is almost certainly less effective than the add always rule (although I have not proved that mathematically).

 

[cruz33]

thanks for your answer!

You are not rounding, which is an approximation that usually creates a small error. You are trying to catch errors, not create them.

A check digit algorithm is an undeviating rule that is designed to catch a high percentage of errors. This one says to add always, not to add sometimes and to subtract sometimes. The add sometimes and subtract sometimes rule is almost certainly less effective than the add always rule (although I have not proved that mathematically).

Ok, I get it! Thanks for your explanation!

 

[cruz33]

good example!

Cruz Sr: son, at your birthday, I'll give you in dollars the next multiple of 10 after your new age
Cruz Jr: oh, so when I turn 13, you'll give me 20 bucks?
Cruz Sr: yes
Cruz Jr: BUT why not give me the previous multiple, 10 bucks?
Cruz Sr: OK; you got a deal!!

This totally makes sense; I understand these concepts better when they are written with words instead of numbers! THANK YOU!