A UPC code has a built-in safeguard to ensure that it is always scanned correctly. The Starbucks bar code below represents a 12 digit string:
7 6 2 1 1 1 8 2 3 3 1 1
If you multiply the 1st,3rd, 5th, 7th, 9th, and 11th by 3, you get 66:
3(7+2+1+8+3+1) = 66 (this would be a good opportunity to illustrate the distributive property)
If you find the sum of the 2nd, 4th, 6th, 8th, 10th, and 12th numbers, you get 14.
(6+1+1+2+3+1)= 14
When we add the two numbers together, the sum is 80 which can be divided by 10. It turns out that most UPC codes follow this "divisible by 10" schema. If a digit was scanned incorrectly, it would be highly unlikely that the resulting sum would be divisible by 10....if it wasn't divisible by 10, it would be flagged as an error and then re-scanned.
I've been skulking around Starbucks taking pictures of UPCs and the baristas are getting a little weirded out. Every UPC I've checked in this store follows the "divisible by 10" protocol. I better stop, though, before I get myself into trouble.
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