History of Science and Engineering Annotation << Back ABOUT NON-DECIMAL REPRESENTATIONS OF FRACTIONAL NUMBERS IN WORKS BY MATHEMATICIANS IN XVII–XVIII CENTURIES Shukhman E.V. The article observes questions related to the introduction and the using of non-decimal fractions in works by mathematicians in XVII–XVIII centuries. The article includes the brief review on the early history of fractional numbers representations in the positional number systems to the middle of the XVII century. We analysed papers by binary arithmetic founder Gottfried Wilhelm Leibniz,his correspondence, unpublished notes from the notebooks of Leonhard Euler, Euler's correspondence with Christian Goldbach. Apparently Leibniz did not have an algorithm for fractions translation to non-decimal number system. L. Euler used such algorithm similar to the modern in the unpublished notes no later than 1739. After in 1745 Euler said his algorithm to C. Goldbach. In the notebooks Euler converted the number π to binary system. He used the binary representation of fractions to calculate the sums of series and infinite products. Euler also was one of the first mathematicians who used latin symbols to denote digits in number systems with radix more than ten. Key words: history of mathematics; non-decimal fractions; translation to non-decimal number systems; Gottfried Wilhelm Leibniz; Leonhard Euler Contacts: E-mail: shukhman.elena@gmail.com Pp. 03-16.