Product code check digits

Steps

1. Ask: do you check your receipt at the shop? Barcodes are so reliable that we trust them.
2. Take a 13-digit barcode and cover the last digit.
3. Write the 12 digits in two rows: the 1st, 3rd, 5th... digits on top and the 2nd, 4th, 6th... on the bottom.
4. Add up the top row. Add up the bottom row and multiply that total by 3. Add the two results together.
5. Take the last digit of that sum. The check digit is what you need to add to reach the next multiple of ten.
6. Compare with the covered digit. Then change one digit and see that the check fails.

Talk about it

• Why is the last digit useful?
• What if two digits swap places?
• Where else do check digits appear, like library books or bank cards?