Can Tersonian Decimal Expansion Represent 1/7 without a Negative Sign?

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Homework Help Overview

The discussion revolves around representing the fraction 1/7 in Tersonian decimal expansion, a concept introduced by the original poster. The original poster attempts to demonstrate that 1/7 can be expressed using a specific decimal format, but raises concerns about the representation of negative values in this system.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition and characteristics of Tersonian decimal expansions, questioning how negative numbers are represented. The original poster presents an example involving the number 1/7 and attempts to relate it to Tersonian notation.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the concept of Tersonian decimal expansions and how they differ from standard decimal representations. Some guidance is offered regarding the structure of Tersonian numbers, but no consensus has been reached on the specific representation of 1/7.

Contextual Notes

There is uncertainty regarding the definition of Tersonian decimal expansions, as participants express confusion about its characteristics and how it applies to the problem at hand. Additionally, the original poster's example includes a potential misinterpretation of the repeating decimal associated with 1/7.

matal
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Homework Statement



1/7=?


Homework Equations





The Attempt at a Solution



Consider $$y=\overline{145827}.0=\dots145827145827145827.0$$,
then $$1000000y=\dots 145827145827000000.0$$ and $$-999999y=145827$$ .
Therefore, $$y=-\dfrac{145827}{999999}$$ . Son in fact $$\overline{145827}.0$$ is a "negative" number.

$$\dfrac{1}{7}=-\overline{145827}.0$$ However, There is no minus in Tersonian decimal expansions?? How can I show 1/7 in Tersonian decimal expansion??
 
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Welcome to PF!

Hi matal! Welcome to PF! :smile:

What's "Tersonian" ? :confused:

(I couldn't find it in wikipedia or google)
 
yes, I searched it too. My teacher said "Here are some problems from Tersonian Elementary School Mathematics Book:" For instance , y=\overline{12}.0 is a Tersonian decimal expansion. Normally, decimal expansions are in after the comma but in tersonian, expansions in before the comma.
 
You mean neither of you watch star trek??!

Should 145827 read 142857 or is that part of the problem too?
 
145827 is not part of the problem. for instance, when you show -1 in tersonian decimal expansion:
you should write " consider a number y= \overline{9}.0=\dots9999.0 . Then 10y= \dots 9990.0 and -9y=9 . Therefore y=-1 so -1=\overline{9}.0" I mean I need a tersonian decimal expansion which equals to 1/7.
 

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