The decimal representation of real numbers

• Autores: A. Kalapodi
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 41, Nº. 7, 2010, págs. 889-900
• Idioma: inglés
• DOI: 10.1080/0020739x.2010.486450
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• Resumen

  • The representation of natural numbers in decimal form is an unequivocal procedure while for the representation of real numbers some ambiguities concerning the existence of infinitely many digits equal to 9 still emerge. One of the most frequently confronted misunderstandings is whether 0.999 � equals 1 or not, and if not what number does this sequence of digits represent. In this review article, the decimal representation of any real number is explicitly presented. In particular, it is investigated whether this representation is unique or not. A condition is given that guarantees the uniqueness of decimal representation for a subset of real numbers, while for the remaining numbers two decimal representations exist. It is also investigated which sequences of digits cannot be accepted as decimal representations of real numbers. Moreover, analogous results are presented in the case where a real number is represented in systems with base n, n being a natural number greater than 1.