The dewey decimal system groups books by

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The DDS divides knowledge into ten main classes. The ten main classes are each divided into ten divisions, and each division into ten sections, giving ten main classes, 100 divisions and 1000 sections. 

Except for general works and fiction, works are classified principally by subject, with extensions for subject relationships, place, time or type of material, producing classification numbers of at least three digits but otherwise of indeterminate length with a decimal point before the fourth digit, where present (e.g. 330 for economics + .9 for geographic treatment + .04 for Europe = 330.94 European economy; 973 for United States + .05 form division for periodicals = 973.05 periodicals concerning the United States generally). 

Books are placed on the shelf in increasing numerical order of the decimal number, e.g. 050, 220, 330, 330.973, 331. When two books have the same classification number the second line of the call number (usually the first letter or letters of the author's last name, the title if there is no identifiable author) is placed in alphabetical order.