### Abstract

Most mathematics teachers are familiar with only base ten decimal numbers. Many of them may know the necessary conditions when a rational fraction may be a finite decimal, an infinite pure recurring decimal or, an infinite mixed recurring decimal under base ten. However, what about decimal numbers with bases other than ten? Will the necessary conditions be the same? What do decimal numbers look like under base two? Since the Future of Mathematics Education links closely with computer structures which use the binary numeral system, it is both interesting and crucial that Mathematics teachers in the future familiarize themselves with decimal numbers under base two. This paper focuses on the representation of proper rational fractions by binary decimals. We narrow our scope to look at only proper fractions where a, b are positive integers with a<b and b not = 0 nor = 1. We would show and prove a theorem specifying the relationships between b and the base n = 2 which determine whether the representation will become either finite decimal, infinite pure recurring decimal or infinite mixed recurring decimal under base n = 2. Decimal numbers with bases other than ten or two will also be explored. Copyright © 2004 author(s).

Original language | English |
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Title of host publication | Proceedings of the international conference: The future of mathematics education |

Editors | Alan ROGERSON |

Place of Publication | Poland |

Publisher | The Mathematics Education into the 21st Century Project |

Pages | 141-144 |

ISBN (Print) | 8391946541 |

Publication status | Published - 2004 |

### Fingerprint

Decimal number

Recurring decimal

Binary

Proper fraction

Numeral

Necessary Conditions

Mathematics Education

Integer

Theorem