menu

arrow_back How do ISBN numbers apply dot products?

by Platinum
(104,456 points)
in Mathematics
17 views

How do ISBN numbers apply dot products?

 

dot product

1 Answer

Best answer
0 like 0 dislike
 
Best answer
Although the system has recently changed, most older books have been assigned a unique 10 -digit number called an International Standard Book or ISBN . The first 9 digits are split into three groups - the first group representing the country or group of countries in which the book originates, the second identifying the publisher, and the third assigned to the book title itself. The tenth and final digit, called a check digit, is computed from the first nine digits and is used to ensure that an electronic transmission of the ISBN, say over the Internet, occurs without error. To explain how this is done, regard the first nine digits of the ISBN as a vector $\mathbf{b}$ in $R^{9}$, and let a be the vector $$ \mathbf{a}=(1,2,3,4,5,6,7,8,9) $$ Then the check digit $c$ is computed using the following procedure: 1. Form the dot product $\mathbf{a} \cdot \mathbf{b}$. 2. Divide $\mathbf{a} \cdot \mathbf{b}$ by 11 , thereby producing a remainder $c$ that is an integer between 0 and 10 , inclusive. The check digit is taken to be $c$, with the proviso that $c=10$ is written as $\mathrm{X}$ to avoid double digits. For example, the ISBN of the brief edition of Calculus, sixth edition, by Howard Anton is $$ 0-471-15307-9 $$ which has a check digit of $9 .$ This is consistent with the first nine digits of the ISBN, since $$ \mathbf{a} \cdot \mathbf{b}=(1,2,3,4,5,6,7,8,9) \cdot(0,4,7,1,1,5,3,0,7)=152 $$ Dividing 152 by 11 produces a quotient of 13 and a remainder of 9 , so the check digit is $c=9 .$ If an electronic order is placed for a book with a certain ISBN, then the warehouse can use the above procedure to verify that the check digit is consistent with the first nine digits, thereby reducing the possibility of a costly shipping error.
by Platinum
(104,456 points)
edited by

Related questions


Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Can you do matrix multiplication using dot products?
1 answer 10 views
Can you do matrix multiplication using dot products?Can you do matrix multiplication using dot products? ...
by MathsGee Platinum
(104,456 points)
asked in Mathematics Jan 13
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What are the basic properties of the inner(dot) product?
1 answer 43 views
What are the basic properties of the inner(dot) product?What are the basic properties of the inner(dot) product? ...
by Maths Genie Bronze Status
(5,362 points)
asked in Mathematics Aug 9, 2021
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Let $a, b$ and $c$ be vectors in $\mathrm{R}^{3}, \times$ denotes the cross product, . the dot product. Which of the following is false?
0 answers 7 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find the dot product of $u = <-5,-6,-2>$ and $v = <-3,10,8>$. Are $u$ and $v$ orthogonal?
0 answers 90 views
Find the dot product of $u = <-5,-6,-2>$ and $v = <-3,10,8>$. Are $u$ and $v$ orthogonal?Find the dot product of $u = &lt;-5,-6,-2&gt;$ and $v = &lt;-3,10,8&gt;$. Are $u$ and $v$ orthogonal? ...
by MathsGee Platinum
(104,456 points)
asked in Mathematics Apr 12, 2021
close

Join the MathsGee Homework Help Q&A club where you get study support for success from our verified experts. Subscribe for only R100 per month or R960 per year.


On the MathsGee Homework Help Q&A learning community, you can:


  1. Ask questions
  2. Answer questions
  3. Comment on Answers
  4. Vote on Questions and Answers
  5. Donate to your favourite users
  6. Create/Take Live Video Lessons

Posting on the MathsGee Homework Help Q&A learning community


  1. Remember the human
  2. Behave like you would in real life
  3. Look for the original source of content
  4. Search for duplicates before posting
  5. Read the community's rules

MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

Management Leadership | MathsGee ZOOM | eBook | H5P