Desimal Berulang untuk suatu Numerator

Affaf, Moh.

APOTEMA : Jurnal Program Studi Pendidikan Matematika
Vol 4 No 2 (2018): APOTEMA: Jurnal Program Studi Pendidikan Matematika

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 𝑚𝑛be 𝑎𝑏with 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 1𝑝is 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 1𝑝is 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 1𝑝is 𝑎𝑏, then 𝐵(𝑝1, 𝑎, 3) is multiply of 10𝑎 − 1. In 2007, study of repeating decimal of 1𝑛is expanded, that 𝑛 dont have to prime greater than 5, but just relatively prime to 10. In this paper, will be investigated property of repeating decimal of 𝑚𝑛with 𝑚 dont have to equal to 1, but enough less than 𝑛and relatively prime to 𝑛.