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rakesh_semwal
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Small Number Game.

05/11/2010 3:53 AM

Here is something interesting, I have tried it with many other denominators and don't get similar results, Numbers at the right side of decimals are not changing They are just shifting there position in circular pattern, Except for the case of denominator = numerator.

And it so happen that 22/7 (pie) is happen to be in the row.

Is it just a coincident? Looking for responses, Please!

1/7= 0.14285714285714285714285714285714--

2/7= 0.2857142857142857142857142857142---

3/7 = 0.42857142857142857142857142857142--

4/7= 0.57142857142857142857142857142857--

5/7= 0.71428571428571428571428571428571--

6/7= 0.85714285714285714285714285714285--

7/7= 1

8/7= 1.1428571428571428571428571428571--

22/7= 3.1428571428571428571428571428571--
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user-deleted-1105
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#1

Re: Small number game.

05/11/2010 3:57 AM

Bad scary numbers <scampers off to hide>
Del

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rakesh_semwal
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#2
In reply to #1

Re: Small number game.

05/11/2010 4:07 AM

You were expected to be the first! Think of a cat and cat is there.
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AussieBob
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#3

Re: Small number game.

05/11/2010 8:28 AM

Hi Rakesh,

No its not coincidental, and

  • 1⁄7 = 1 × 0.142857... = 0.142857...
  • 3⁄7 = 3 × 0.142857... = 0.428571...
  • 2⁄7 = 2 × 0.142857... = 0.285714...
  • 6⁄7 = 6 × 0.142857... = 0.857142...
  • 4⁄7 = 4 × 0.142857... = 0.571428...
  • 5⁄7 = 5 × 0.142857... = 0.714285.. Easiest explanation is probably http://en.wikipedia.org/wiki/Repeating_decimal
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rakesh_semwal
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#5
In reply to #3

Re: Small number game.

05/11/2010 9:59 AM

Thank you for putting views.

Actually multiplying them with integer is as good as changing numerator, Interesting thing is no other denominator give this kind of results.except for 7 and multiple of 7.
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Mikerho
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#4

Re: Small number game.

05/11/2010 9:54 AM

But 22/7 is not Pi. Pi is not a repeating decimal, it is an irrational number, meaning that it cannot be expressed as a fraction.

Interesting series though.

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rakesh_semwal
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#6
In reply to #4

Re: Small number game.

05/11/2010 10:26 AM

Yes but thats is the best choice with use for pi.
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cingold
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#12
In reply to #4

Re: Small number game.

05/12/2010 7:41 AM

"Pi is not a repeating decimal, it is an irrational number, meaning that it cannot be expressed as a fraction."

Circumference divided by diameter?

C/d

That's a fraction right?
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rakesh_semwal
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#13
In reply to #12

Re: Small number game.

05/12/2010 8:53 AM

Hi cingold

22/7 is one of the rational approximation for pi, No one know the value of pi to perfection, You may know more precise value than of 22/7 but Even that can be Challenged by someone else.

This can not be wrong.

If you solve 22/7 Thats going to give you repeating decimals. But thats not going to stop its use for pi, specially where lower precision is required.
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AussieBob
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#20
In reply to #13

Re: Small number game.

05/14/2010 1:00 AM

"No one know the value of pi to perfection"

Yes we do!!

or, 3 1/2Pi

Sorry couldn't resist. (with acknowledgement to the original image poster some time ago)
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rakesh_semwal
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#21
In reply to #20

Re: Small number game.

05/14/2010 5:40 AM

They should have made it square in shape to stay away from the dispute over pi.
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cingold
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#23
In reply to #13

Re: Small number game.

05/14/2010 8:23 AM

There's a reason I made my response an "off-topic" response. Don't look into it because I was just trying to make a joke. Perhaps it didn't land so oh well.
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rakesh_semwal
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#24
In reply to #23

Re: Small number game.

05/14/2010 10:00 AM

Sorry if any ting that got misunderstood.
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LAA_Lucke
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#18
In reply to #12

Re: Small number game.

05/12/2010 2:15 PM

"C/D"

This is not (pie)! C is derived using pie in the first place.

C = pie x D

To calculate C (circumference) was the problem in the first place.

Since you cannot obtain C except an approximate value of it, the fraction cannot be written the way you put it. CQFD
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cingold
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#22
In reply to #18

Re: Small number game.

05/14/2010 8:20 AM

First off. I was just joking about the fraction. I took Mikerho's statement out of context.

Second:

http://en.wikipedia.org/wiki/Pi

"Antiquity

That the ratio of the circumference to the diameter of a circle is the same for all circles, and that it is slightly more than 3, was known to Ancient Egyptian, Babylonian, Indian and Greek geometers. The earliest known textually evidenced approximations date from around 1900 BC; they are 25/8 (Babylonia) and 256/81 (Egypt), both within 1% of the true value.[8] The Indian text Shatapatha Brahmana gives π as 339/108 ≈ 3.139."

There's plenty of other quotes I can take from here but calculating C was never the problem. C was measured as a perimeter and then compared to the diameter.

Pi is the ratio between circumference and diameter.
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Tornado
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#19
In reply to #12

Re: Small number game.

05/14/2010 12:29 AM

No, C/d is not a fraction. Either C or d (or both) is a non-integer.

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Maths_Physics_Maniac
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#7

Re: Small Number Game.

05/11/2010 10:58 PM

This is my understanding for what it is worth:-

There are basically 2 types of numbers, rational and irrational.

Rational numbers can be expressed as a fraction which is basically the ratio of two integers. I.E. 22 divided by 7 (This is used sometimes as an approximation for Pi but it does NOT equal Pi)

These rational numbers can also be expressed in decimal form which always results in a finite or repeating decimal such as those examples you have shown.

Irrational numbers such as Pi can never be represented by the ratio of two integers no matter how big you make these integers. Also the irrational number when written in decimal form will never show any repition pattern after the decimal point.

This is the very fact that makes such a number irrational.
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rakesh_semwal
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#10
In reply to #7

Re: Small Number Game.

05/12/2010 1:59 AM

Hello, Maths_Physics_Maniac.

Thank you for writing.

I am not saying that it has to anything with pi, As I said it happened to be so that 22/7 (we use for pi) is in row.

Probably I could not express myself rightly in original post so please have a look on my reply to tornado.

Regards.
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Tornado
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#8

Re: Small Number Game.

05/12/2010 12:47 AM

1/7 is not the only such number, anyway.

For any prime number p other than 2 or 5 (which are factors of 10), 1/p is a repeating decimal in which the block of repeating digits is at most (p-1) digits long.

For example:

1/13 = 0.076923 (the underlined part repeated indefinitely).

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rakesh_semwal
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#9
In reply to #8

Re: Small Number Game.

05/12/2010 1:46 AM

Thank you for views.

1/13 = 0.076923 (the underlined part repeated indefinitely).

You are right on your statement, but in the case you shown moment we change the numerator from 1 to 2 we can see the change of series from 076923 to 0.153846. where as in the case of denominator 7, series is always going to be 142857. thats what statement I am trying to make, which perhaps I could not do in the original post.

You can see the difference in below example.

1/13= 0.076923076923076923076923...... 1/7 =0.14285714285714285714285714

2/13= 0.153846153846153846153846....... 2/7 =0.28571428571428571428571428

3/13= 0.230769230769230769230769 .......3/7 = 0.42857142857142857142857142

(series changes)........................................... (No change in series)

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Anonymous Poster
#14
In reply to #9

Re: Small number game.

05/12/2010 9:01 AM

Look here

As per this,

the number

( bp-1 -1)/p is cyclic

b=10

p=7,17,19,23,29,...

the numbers are 142857,

check 1/17, 1/19, etc with the repetitions at

142857,

588235294117647,

52631578947368421,

434782608695652173913,

344827586206896551724137931 and so on

BTW the best ones never talked about are 1/3, 1/9 ?
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Randall
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#11

Re: Small number game.

05/12/2010 4:17 AM

Did you follow AussieBob's link. There is a sub link to the 142857 number.

Here's a small puzzle for you. Replace the letters with digits:-

EVE
---- = TALKTALKTALKTALK............. (repeats for ever)
DID

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rakesh_semwal
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#15
In reply to #11

Re: Small number game.

05/12/2010 9:08 AM

Thank you,

Yes I have seen Both, look magical.

any clue for EVE/DID?

I have tried with decimal systam. is that ok? dont get any talk there.
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Anonymous Poster
#16
In reply to #15

Re: Small number game.

05/12/2010 9:36 AM

242/303 = =0.79867986...

Look at #14 (and also at long primes in Wiki)
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Randall
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#17
In reply to #15

Re: Small number game.

05/12/2010 12:21 PM

Sorry should have read:-

EVE
---- = •TALKTALKTALKTALK............. (repeats for ever)
DID

It is decimal. Guest's answer is correct, but try not to look at it.

Just notice that 1/9 = .11111.....
1/99 = 0.0101010101.....
1/999 = 0.001001001001....
1/9999 = 0.0001000100010001

So 0.TALKTALKTALK..........=TALK/9999

work from there.

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