Answer to Question #146160 in Financial Math for Paul aguila

Question

1. The Library Publishing house want to know the ISBN check digit of Math Power
book with the ISBN: 978-971-0499-31-?
2.Jay's restaurant wants to know if the credit card use by the customer is valid.the credit card number is 4000 0012 3456 7899

Answer 1

1) Method to find ISBN-13 check digit:

The calculation of an ISBN-13 check digit begins with the first 12 digits of the thirteen-digit ISBN(thus excluding the check digit itself). Each digit, from left to right, is alternately multiplied by 1 or 3, then those products are summed modulo 10 to give a value ranging from 0 to 9. Subtracted from 10, that leaves a result from 1 to 10. A zero(0) replaces a ten(10), so, in all cases, a single check digit results.

Formally, using modular arithmetic, we can say:

(x₁ + 3x₂ + x₃ + 3x₄ + x₅ + 3x₆ + x₇ + 3x₈ + x₉ + 3x₁₀ + x₁₁ +3x₁₂ + x₁₃ ) 0 (mod 10).

find ISBN-13 check digit of 978-971-0499-31-

s=(9x1) +(7x3) + (8x1) + (9x3) + (7x1) + (1x3) + (0x1) + (4x3) + (9x1) + (9x3)+ (3x1)+ (1x3)

=9 + 21 + 8 + 27 + 7 + 3 + 0 + 12 + 9 + 27 + 3 + 3

=129

129/10=12 remainder 9

10 - 9= 1

Thus the check digit is 9m and the complete sequence is ISBN 978-971-0499-31-1

2) Here is the step by step procedure to validate the credit card number:

4000 0012 3456 7899

Step-1: Starting with the check digit double the value of every other digit (right to left every 2nd digit)

Step 2 - If doubling of a number results in a two digits number, add up the digits to get a single digit number. This will result in eight single digit numbers.

8+0+0+0+0+0+2+2+6+4+1+6+5+8+9+9=60

If the final sum is divisible by 10, then the credit card number is valid. If it is not divisible by 10, the number is invalid.

In our case as 60/10=6, divisible by 10, hence the given credit card number is valid.