Digital root of a rational number

Keywords:

Congruence, Digital root, Divisibility, Orbit and Sum of digits function

Abstract

The digital roots S* (x), of a n positive integer is the digit 0 ≤ b ≤ 9 obtained through an iterative digit sum process, where each iteration is obtained from the previous result so that only the b digit remains. For example, the iterated sum of 999999 is 9 because 9 + 9 + 9 + 9 + 9 + 9 = 54 and 5 + 4 = 9. The sum of the digits of a positive integer, and even the digital roots, is a recurring subject in mathematical competitions and has been addressed in several papers, for example in Ghannam (2012), Ismirli (2014) or Lin (2016). Here we extend the application Sast to a positive rational number x with finite decimal representation. We highlight the following result: given a rational number x, with finite decimal representation, and the sum of its digits is 9, so when divided x by powers of 2, the number resulting also has the sum of its digits 9. Fact that also occurs when the x number is divided by powers of 5. Similar results were found when the x digit sum is 3 or 6.

Author Biographies

Deyfila da Silva Lima, Universidade Federal do Tocantins, Arraias, TO

Possui graduações em Pedagogia e em Licenciatura em Matemática pela Universidade Federal do Tocantins.

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2021-03-01

How to Cite

Costa, E. A., Lima, D. da S., Mesquita, Élis G. da C., & Souza, K. C. O. (2021). Digital root of a rational number. Ciência E Natura, 43, e12. https://doi.org/10.5902/2179460X41972

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