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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2016.tde-05102016-085553
Document
Author
Full name
Fernanda Martinez Menezes
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Pires, Benito Frazão (President)
Artioli, Vanessa Rolnik
Manoel, Miriam Garcia
Nascimento, Marcelo José Dias
Title in Portuguese
Propriedades da expansão decimal
Keywords in Portuguese
Dígitos
Expansão decimal
Números racionais e irracionais
Abstract in Portuguese
Este trabalho tem como objetivo principal o estudo da expansão decimal dos números reais. Primeiramente provamos que todo número real possui ao menos uma expansão decimal. Na sequência, um método para encontrar a expansão decimal de um número entre 0 e 1 é apresentado, bem como um estudo sobre a expansão decimal de números racionais e irracionais. Em seguida, o estudo apresenta métodos que permitem encontrar aproximações racionais de números irracionais, além dos erros cometidos por essas aproximações. Na parte final, por seu turno, o foco do trabalho recai sobre a análise da regularidade (frequência) dos dígitos das expansões decimais.
Title in English
Properties of the decimal expansion
Keywords in English
Decimal expansion
Digits
Rational and irrational numbers
Abstract in English
This work has as main objective the study of the decimal expansion of the real numbers. First we prove that every real number has at least one decimal expansion. Further, a method to find the decimal expansion of real numbers between 0 and 1 is provided as well as a the study of the decimal expansion of rational and irrational numbers. Next, the study presents methods that provide rational approximations to irrational numbers, in addition to the errors committed by these approximations. At the end, by its turn, the focus of the work is put on the analysis of the regularity (frequency) of the digits of the decimal expansion.
 
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Publishing Date
2016-10-05
 
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