Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-06-27T21:01:10.157Z Has data issue: false hasContentIssue false
  • English
  • Français

On Tertial, Quintal, Etc., Fractions

Published online by Cambridge University Press:  15 September 2017

Lt.-Col. Allan Cunningham
Get access Rights & Permissions [Opens in a new window]

Extract

1. Def. The reciprocal (1/N) of any number (N) will be termed a Binal, Tertial, Quintal, ... Decimal, ... r-mal fraction, when expressed in the scale whose radix is r = 2, 3, 4, ... 10, ... r respectively. In this paper the developments will be given for the most part in a general form in the r-scale; the examples will be in the scales of r = 3 and 5. The notation is similar to that of ordinary decimals. Thus (see Tables at end):

Type
Research Article
Information
The Mathematical Gazette , Volume 6 , Issue 92 , May 1911 , pp. 63 - 67
Copyright
Copyright © Mathematical Association 1911

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

* The subject of Binal Fractions was treated of in the author’ s previous paper on Binal Fractions (Math. Gazette, vol. iv., 1908, pp. 259-267). For facility of comparison, the present paper is written in the same style as the former, and the corresponding Articles and Results bear the same reference numbers. [The author’ s acknowledgments are due to Mr. M. J. Woodall, A.K.C.Sc, for help in reading the proof sheets.]

page note 65 * In what follows ξ is always supposed known. For prime, and powers of prime, moduli (N = p or pn ) < 1000, it can be easily found from Jacobi’s Canon Arithmeticus.

† Compare Tables at end.

‡ The reduction of 001001 to 001 is due to the fact that N 1=(33-1), for which ξ=3.