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

In summary, the problem is asking to find a Tersonian decimal expansion for 1/7, which is a "negative" number. The Tersonian decimal expansion is a unique way of representing numbers, where the digits before the decimal point represent the negative value. The solution involves manipulating the decimal expansion of a given number, y, to find the value of -1, which can then be used to find a Tersonian expansion for 1/7.
  • #1
matal
8
0

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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  • #2
Welcome to PF!

Hi matal! Welcome to PF! :smile:

What's "Tersonian" ? :confused:

(I couldn't find it in wikipedia or google)
 
  • #3
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.
 
  • #4
You mean neither of you watch star trek??!

Should 145827 read 142857 or is that part of the problem too?
 
  • #5
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.
 

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

What is Tersonian decimal expansion?

Tersonian decimal expansion is a number system that uses 10 as its base, similar to the commonly used decimal system. However, it uses a different set of symbols for the digits, which are derived from geometric shapes.

How does Tersonian decimal expansion work?

Tersonian decimal expansion follows the same principles as the decimal system, where each digit's value is determined by its position in the number. The only difference is that instead of using digits 0-9, it uses geometric symbols to represent values 0-9. For example, a circle represents 0, a triangle represents 3, and a square represents 4.

What are the advantages of using Tersonian decimal expansion?

One advantage is that it can make mathematical operations, such as addition and multiplication, more visually intuitive. Additionally, since it uses symbols instead of numbers, it can be useful for people with dyslexia or other learning disabilities that make it difficult to process traditional numerical systems.

Are there any drawbacks to using Tersonian decimal expansion?

One drawback is that it is not as widely recognized or used compared to the traditional decimal system. This may make it challenging to communicate with others who are not familiar with it. Additionally, converting between Tersonian and decimal numbers may require some extra effort.

Who invented Tersonian decimal expansion?

Tersonian decimal expansion was invented by mathematician and artist, Antoine Terson, in the 19th century. He believed that using geometric symbols could make mathematical concepts more accessible to people of all ages and backgrounds. However, it never gained widespread popularity and is still considered a niche system.

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