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On Tertial, Quintal, Etc., Fractions

Published online by Cambridge University Press:  15 September 2017

Lt.-Col. Allan Cunningham
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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

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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.