Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-06-19T09:22:59.190Z Has data issue: false hasContentIssue false
  • English
  • Français

Some properties of repetends

Published online by Cambridge University Press:  01 August 2016

N. J. Armstrong  and
R. J. Armstrong
N. J. Armstrong
Affiliation:
Myrengv. 34, 9011 Tromsø, Norway
R. J. Armstrong
Affiliation:
Faculty of Science, University of Tromsø, 9037 Tromsø, Norway
Get access Rights & Permissions [Opens in a new window]

Extract

We wish to discuss some aspects of repetends, the repeating sequence of digits in the expansion of a fraction (for illuminating introductions to the subject see [1, 2]). For the most part we restrict consideration here to fractions with a prime denominator. But we do consider the general condition for the length of repetends and examine some special cases when the base of the number system is varied. An illustration of the use of other bases than 10 is given. Then we consider the multiplication of repetends and show a connection with group theory, giving an old result by a new twist.

Type
Articles
Information
The Mathematical Gazette , Volume 87 , Issue 510 , November 2003 , pp. 437 - 443
Copyright
Copyright © The Mathematical Association 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Silvester, J.R., Decimal dèjà vu, Math. Gaz. 83 (November 1999) pp. 453–463.Google Scholar
2. Conway, J.H. and Guy, R.K., The book of numbers, Copernicus (1996).Google Scholar
3. Armstrong, N.J. and Armstrong, R.J., An observation concerning repetends, Math. Gaz. 81 (March 1997) pp. 101–104.Google Scholar
4. Ledermann, W., Introduction to group theory, Oliver and Boyd (1973).Google Scholar
5. Barr, L.J.T., Edinburgh, Private communication.Google Scholar
6. Yates, S., Repunits and Repetends, published privately by the author, Delray Beach, Florida USA (1982).Google Scholar