Sure! I can provide you with five examples and questions related to ISBN-13 (International Standard Book Number) and explain the steps to solve them. Here they are:
Example 1:
Question: Determine the check digit for the ISBN-13 number 978316148410?
Solution:
Step 1: Multiply each digit of the ISBN-13 number alternately by 1 and 3, starting from the first digit.
9×1 + 7×3 + 8×1 + 3×3 + 1×1 + 6×3 + 1×1 + 4×3 + 8×1 + 4×3 + 1×1 + 0×3 = 9 + 21 + 8 + 9 + 1 + 18 + 1 + 12 + 8 + 12 + 1 + 0 = 100
Step 2: Take the sum from Step 1 and find the remainder when divided by 10.
100 % 10 = 0
Step 3: If the remainder obtained in Step 2 is 0, then the check digit is 0. Otherwise, subtract the remainder from 10 to get the check digit.
Since the remainder is 0, the check digit is 0.
Example 2:
Question: Find the missing digit in the ISBN-13 number 978-3-16-148410-?
Solution:
Step 1: Multiply each digit of the ISBN-13 number alternately by 1 and 3, starting from the first digit.
9×1 + 7×3 + 8×1 + 3×3 + 1×1 + 6×3 + 1×1 + 4×3 + 8×1 + 4×3 + 1×1 + ?×3 = 9 + 21 + 8 + 9 + 1 + 18 + 1 + 12 + 8 + 12 + 1 + 3×? = 100
Step 2: Take the sum from Step 1 and find the remainder when divided by 10.
100 % 10 = 0
Step 3: If the remainder obtained in Step 2 is 0, then the missing digit is 0. Otherwise, subtract the remainder from 10 to get the missing digit.
Since the remainder is 0, the missing digit is 0.
Example 3:
Question: Determine if the ISBN-13 number 978316148410 is valid or not?
Solution:
Step 1: Multiply each digit of the ISBN-13 number alternately by 1 and 3, starting from the first digit.
9×1 + 7×3 + 8×1 + 3×3 + 1×1 + 6×3 + 1×1 + 4×3 + 8×1 + 4×3 + 1×1 + 0×3 = 9 + 21 + 8 + 9 + 1 + 18 + 1 + 12 + 8 + 12 + 1 + 0 = 100
Step 2: Take the sum from Step 1 and find the remainder when divided by 10.
100 % 10 = 0
Step 3: If the remainder obtained in Step 2 is 0, then the ISBN-13 number is valid. Otherwise, it is not valid.
Since the remainder is 0, the ISBN-13 number 978316148410 is valid.
Example 4:
Question: Determine if the ISBN-13 number 978316148413 is valid or not?
Solution:
Step 1: Multiply each digit of the ISBN-13 number alternately by 1 and 3, starting from the first digit.
9×1 + 7×3 + 8×1 + 3×3 + 1×1 + 6×3 + 1×1 + 4×3 + 8×1 + 4×3 + 1×1 + 3×3 = 9 + 21 + 8 + 9 + 1 + 18 + 1 + 12 + 8 + 12 + 1 + 9 = 99
Step 2: Take the sum from Step 1 and find the remainder when divided by 10.
99 % 10 = 9
Step 3: If the remainder obtained in Step 2 is 0, then the ISBN-13 number is valid. Otherwise, it is not valid.
Since the remainder is 9, the ISBN-13 number 978316148413 is not valid.
Example 5:
Question: Find the missing digit in the ISBN-13 number 978-3-16-14841-?
Solution:
Step 1: Multiply each digit of the ISBN-13 number alternately by 1 and 3, starting from the first digit.
9×1 + 7×3 + 8×1 + 3×3 + 1×1 + 6×3 + 1×1 + 4×3 + 8×1 + 4×3 + 1×1 + ?×3 = 9 + 21 + 8 + 9 + 1 + 18 + 1 + 12 + 8 + 12 + 1 + 3×? = 99
Step 2: Take the sum from Step 1 and find the remainder when divided by 10.
99 % 10 = 9
Step 3: If the remainder obtained in Step 2 is 0, then the missing digit is 0. Otherwise, subtract the remainder from 10 to get the missing digit.
Since the remainder is 9, the missing digit is 1.
I hope these examples and solutions help you understand how to work with ISBN-13 numbers and solve related problems step by step. Let me know if you have any further questions!
