Desimal Berulang untuk suatu Numerator

  • Moh. Affaf STKIP PGRI BANGKALAN

Abstract

Let 𝑛 denote a positive integer relatively prime to 10 and 𝑚 be natural
number less than 𝑛 and relatively prime to 𝑛. Let the period of 𝑚
𝑛
be 𝑎𝑏
with 𝑏 > 1. Break the repeating block of 𝑎𝑏 digits up into 𝑏 sub blocks,
each of length 𝑎, and let 𝐵(𝑛𝑚, 𝑎, 𝑏) denote the sum of these 𝑏 blocks.
In 1836 has been proved and re-proofed in 2013 that if 𝑝 is a prime
greater than 5, and the period of 1
𝑝
is 2𝑎, then 𝐵(𝑝1, 𝑎, 2) = 10𝑎 − 1. In
2004, has been showed that if 𝑝 is a prime greater than 5, and the period
of 1
𝑝
is 3𝑎, then 𝐵(𝑝1, 𝑎, 3) = 10𝑎 − 1. In 2005, also was showed that if
𝑝 is a prime greater than 5, and the period of 1
𝑝
is 𝑎𝑏, then 𝐵(𝑝1, 𝑎, 3) is
multiply of 10𝑎 − 1. In 2007, study of repeating decimal of 1
𝑛
is
expanded, that 𝑛 don't have to prime greater than 5, but just relatively
prime to 10. In this paper, will be investigated property of repeating
decimal of 𝑚
𝑛
with 𝑚 don't have to equal to 1, but enough less than 𝑛
and relatively prime to 𝑛.

Published
Jul 31, 2018
How to Cite
AFFAF, Moh.. Desimal Berulang untuk suatu Numerator. APOTEMA : Jurnal Program Studi Pendidikan Matematika, [S.l.], v. 4, n. 2, p. 19-26, july 2018. ISSN 2580-9253. Available at: <http://jurnal.stkippgri-bkl.ac.id/index.php/APM/article/view/485>. Date accessed: 12 dec. 2018.