"To determine:The check digit of an ISSN that..." solved and explained

High School
Algebra
Algebra II
Polynomial factorization

iohanetc

Answered question

2021-03-07

To determine:The check digit of an ISSN that has these initial 7 digits 1570-868

Answer & Explanation

Brittany Patton

Skilled2021-03-09Added 100 answers

Formula used:
An ISSN consists of two blocks of four digits. The last digit in the second block is a check digit. This check digit is determined by the congruence

d_{8} \equiv 3 d_{1}, + 4 d_{2} + 5 d_{3} + 6 d_{4} + 7 d_{5} + 8 d_{6} + 9 d_{7} \pm o d {11}

When

d_{8} \equiv 10 \pm o d {11}

, we use the letter X to represent dg in the code.
Insert the digits of 1570 — 868 into the congruence

d_{8} \equiv 3 d_{1}, + 4 d_{2} + 5 d_{3} + 6 d_{4} + 7 d_{5} + 8 d_{6} + 9 d_{7} \pm o d {11}

.
This gives,

d_{8} \equiv 3 \cdot 1 + 4 \cdot 5 + 5 \cdot 7 + 6 \cdot 0 + 7 \cdot 8 + 8 \cdot 6 + 9 \cdot 8 \pm o d {11}

d_{8} \equiv 3 + 20 + 35 + 0 + 56 + 48 + 72 \pm o d {11}

d_{8} \equiv 234 \pm o d {11}

d_{8} \equiv 3 \pm o d {11}

Hence, the check digit is 3.

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