1. Analyzing Numerical Data: Validating Identification Numbers
Credit Card Numbers
UPC Codes

2. UPC CODE

3. UPC Code
Steps: Underline the odd positions. Then add them up. Take that total and multiply by 3. Then add the even position numbers up. Add the totals together.
The underline number is the odd digits. Add them up = 20. Then multiply them by 3, 20*3 =60. Then add the other numbers =30. So, 60+30=90. Since the last digit is 0 it is a valid UPC Code.

4. Example 2 Work: 9 8 7 6 5 4 3 2 1 0 9 8 9+7+5+3+1+9 = 34 34*3 =102
Then add the remaining numbers:
=28
So, =130
It does=0 so therefore it is a valid UPC Code.

5. Determine the Check Digit
=23
23(3) =69
=21
69+21=90
So, Valid UPC Code!

6. Learning About Credit Cards
Identification numbers are present everywhere in society. Today’s identification numbers are more sophisticated than those introduced years earlier (for example, Social Security numbers). Today’s numbers have a check digit to partially ensure that they have been correctly scanned or entered into a computer.
Credit cards have 16-digit numbers, of which the first 15 digits identify the credit card
and the sixteenth digit is the check digit. The following figure shows the significance of
the digits: MII stands for major industry identifier; 4 and 5 indicate “Banking and Financial.” VISA cards begin with 4 and MasterCard cards with 5.

7. Learning About Credit Cards
1. MasterCard numbers begin with 51, 52, 53, 54, or 55. What is the maximum number of credit cards that MasterCard can issue?
=𝟓∙ 𝟏𝟎 𝟏𝟑 =𝟓𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎

8. The “Check Digit”
A check digit is used to help validate credit card numbers. The credit card companies use the Codabar method to determine the check digit. This method consists of the following steps: a. Add the digits in the odd-numbered positions and double this total. b. Add the number of odd-position digits that are more than 4 to the total. c. Add the even-position digits. d. Choose a check digit that makes this calculation total a number whose final digit is 0. NOTE: Libraries, shipping/receiving companies, and blood banks also use the Codabar method.
2. What is the check digit (d) for the VISA card d?
2( ) + 4 [6, 5, 7, 9] + ( d )
= 2(35) d = 97 + d ,
so d = 3 for the total to be a multiple of 10.

9. The “Check Digit”
A check digit is used to help validate credit card numbers. The credit card companies use the Codabar method to determine the check digit. This method consists of the following steps: a. Add the digits in the odd-numbered positions and double this total. b. Add the number of odd-position digits that are more than 4 to the total. c. Add the even-position digits. d. Choose a check digit that makes this calculation total a number whose final digit is 0. NOTE: Libraries, shipping/receiving companies, and blood banks also use the Codabar method.
4. find out whether this VISA card is a valid number:
2( ) ( ) =
2(20) =
65, which does not end in 0 so this is NOT a valid cc#.

11. Learning About Credit Cards
Interesting Fact: The Codabar method detects 98% of all transposition errors.