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

[matal]

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??

 

[tiny-tim]

Welcome to PF!

Hi matal! Welcome to PF!

What's "Tersonian" ?

(I couldn't find it in wikipedia or google)

 

[matal]

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.

 

[Martin Rattigan]

You mean neither of you watch star trek??!

Should 145827 read 142857 or is that part of the problem too?

 

[matal]

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.