# Desimal Berulang untuk suatu Numerator

### 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.

**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: 18 oct. 2018.