412.0.10 ok so going with dot product with 07312400508

[karush]

Use the UPC scheme to determine the check digit for the number $07312400508$.

here is the example from the book
View attachment 8330
ok so going with dot product with 07312400508
\begin{align*}\displaystyle
&\quad (0731 2 4 0 0 5 0 8)\cdot(3,1,3,1,3,1,3,1,3)\\
&= 0\cdot3+7\cdot1
+3\cdot3+1\cdot1
+2\cdot3+4\cdot1
+0\cdot3+0\cdot1
+5\cdot3+0\cdot1
+8\cdot3 \\
&=7+9+1+6+4+15+24\\
&=66\\
66mod10&=6
\end{align*}

so far?? but the number only has 11 digits

 

[Opalg]

ok so going with dot product with 07312400508
\begin{align*}\displaystyle
&\quad (0731 2 4 0 0 5 0 8)\cdot(3,1,3,1,3,1,3,1,3)\\
&= 0\cdot3+7\cdot1
+3\cdot3+1\cdot1
+2\cdot3+4\cdot1
+0\cdot3+0\cdot1
+5\cdot3+0\cdot1
+8\cdot3 \\
&=7+9+1+6+4+15+24\\
&=66\\
66\pmod{10}&=6
\end{align*}

so far?? but the number only has 11 digits

That is correct so far. You now have to add a twelfth digit so as to make the checksum zero$\pmod{10}$.

 

[karush]

That is correct so far. You now have to add a twelfth digit so as to make the checksum zero$\pmod{10}$.

What would be the 12th digit?

 

[Opalg]

What would be the 12th digit?

What do you have to add to 66 to get a multiple of 10?