Question

The first nine digits of the ISBN-10 of the European version of the fifth edition of this book are$\mathbf{0}\mathbf{-}\mathbf{07}\mathbf{-}\mathbf{119881}$.What is the check digit for that book?

Short answer

Thus, the check digit is4

Step-by-step solution

Step 1

$$\begin{gathered} \mathbf{0}\mathbf{-}\mathbf{07}\mathbf{-}\mathbf{119881} \\ \begin{array}{r}{\mathbf{x}}_{\mathbf{1}}\mathbf{=}\mathbf{0}\\ {\mathbf{x}}_{\mathbf{2}}\mathbf{=}\mathbf{0}\\ {\mathbf{x}}_{\mathbf{3}}\mathbf{=}\mathbf{7}\\ {\mathbf{x}}_{\mathbf{4}}\mathbf{=}\mathbf{1}\\ \\ {\mathbf{x}}_{\mathbf{5}}\mathbf{=}\mathbf{1}\\ {\mathbf{x}}_{\mathbf{6}}\mathbf{=}\mathbf{9}\\ {\mathbf{x}}_{\mathbf{7}}\mathbf{=}\mathbf{8}\\ {\mathbf{x}}_{\mathbf{8}}\mathbf{=}\mathbf{8}\\ {\mathbf{x}}_{\mathbf{9}}\mathbf{=}\mathbf{1}\end{array} \end{gathered}$$

For a ISBN-10 code ${\mathbf{x}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{2}}\mathbf{\dots }{\mathbf{x}}_{\mathbf{10}}$the check digit is calculated using the following expression:

${\mathbf{x}}_{\mathbf{10}}\mathbf{\sum }_{\mathbf{i}\mathbf{=}\mathbf{1}}^{\mathbf{9}}\mathbf{ }{\mathbf{ix}}_{\mathbf{i}}\mathbf{(}\mathbf{mod}\mathbf{11}\mathbf{)}$

Step 2

Use this expression to calculate the check digit

$$\begin{gathered} {\mathit{x}}_{\mathbf{10}}\mathbf{=}\mathbf{1}\mathbf{\times }\mathbf{0}\mathbf{+}\mathbf{2}\mathbf{\times }\mathbf{0}\mathbf{+}\mathbf{3}\mathbf{\times }\mathbf{7}\mathbf{+}\mathbf{4}\mathbf{\times }\mathbf{1}\mathbf{+}\mathbf{5}\mathbf{\times }\mathbf{1}\mathbf{+}\mathbf{6}\mathbf{\times }\mathbf{9}\mathbf{+}\mathbf{7}\mathbf{\times }\mathbf{8}\mathbf{+}\mathbf{8}\mathbf{\times }\mathbf{8}\mathbf{+}\mathbf{9}\mathbf{\times }\mathbf{1}\mathbf{mod} \\ \mathbf{=}\mathbf{0}\mathbf{+}\mathbf{0}\mathbf{+}\mathbf{21}\mathbf{+}\mathbf{4}\mathbf{+}\mathbf{5}\mathbf{+}\mathbf{54}\mathbf{+}\mathbf{56}\mathbf{+}\mathbf{64}\mathbf{+}\mathbf{9}\mathbf{mod}\mathbf{11} \\ \mathbf{=}\mathbf{213}\mathbf{mod}\mathbf{11} \\ \mathbf{=}\mathbf{4} \end{gathered}$$