# Desimal Berulang untuk suatu Numerator

• Moh. Affaf STKIP PGRI BANGKALAN
Keywords: Decimal Representation, Midy's Theorem, Repeating Decimal.

### 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.

### Downloads

Download data is not yet available.
Published
2018-07-31
Section
Articles