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this article describes the chain fractions as another method of presentation of the number. chain fractions is a special section of the theory of numbers, which is rarely studied in the school or at the university. in spite of the factthey are of great importance and application in our life. chain fraction is the decomposition of any actual numbers in the set of numbers, finite or infinite.the passage describes the brief history of chain fractions, due to the difference between the finite and the infinite chain fractions. we prove theorem of singularity decomposition in a fraction. 
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