?
Solved

Stuttering calculator

Posted on 2004-11-02
13
Medium Priority
?
323 Views
Last Modified: 2008-02-01
Ok, take your average desk calculator.

type :  10 / 3 = = = =

Any reasonable explanation for the sequence you get?

0
Comment
Question by:grg99
  • 4
  • 3
  • 2
  • +2
13 Comments
 
LVL 31

Expert Comment

by:GwynforWeb
ID: 12475998
Clearly 10 is being repeatedly by 3. For binary operations eg a*b,  a/b, this is the way I think it works.  I believe they have 2 registers holding the left hand value (displayed) and 1 holding the right hand. When = is hit  (left) operator (right) is evaluated and placed in the display (ie the  left register) and the right  is unchanged. Repeatedly hitting = continuously divides the display value by the right value in this case 3
0
 
LVL 22

Author Comment

by:grg99
ID: 12476273
yesbut how to explain the interesting numbes that pop up:


3.3333333333333333333333333333333

1.1111111111111111111111111111111

0.37037037037037037037037037037037

0.12345679012345679012345679012346

0
 
LVL 27

Expert Comment

by:aburr
ID: 12476827
What's so special about that. Your last lint is missing an 8.

Seriously, you have found an interesting set of digits. I do not beleive there is any special reasoning behind them.
It is interesting to note that whenever you divide two intergers you will get an answer in which the digits will eventually repeat themselves.
0
Concerto's Cloud Advisory Services

Want to avoid the missteps to gaining all the benefits of the cloud? Learn more about the different assessment options from our Cloud Advisory team.

 
LVL 3

Expert Comment

by:Andrea Ercolino
ID: 12477775
its simpler, just divide 10 / 81 ;-)))
0
 
LVL 27

Expert Comment

by:aburr
ID: 12477944
but you miss the other interesting strings
0
 
LVL 3

Expert Comment

by:Andrea Ercolino
ID: 12478036
0,098765432098765432098765432098765... = 8 / 81 ;-)))
0
 
LVL 3

Expert Comment

by:Andrea Ercolino
ID: 12478220
can be shown that the length of the repeating substring in <<1 / n>> is a divisor of the totient of <<n>>

in this case, <<9>> is a divisor of <<Phi( 81 ) = 81 - 27 = 54>>
0
 
LVL 3

Expert Comment

by:Andrea Ercolino
ID: 12478275
some primes <<p>> have the longest repeating substring <<p - 1>>, being <<7>> the smallest one
<<1 / 7 = 0,14285714285714285714285714285714...>>
0
 
LVL 18

Expert Comment

by:JR2003
ID: 12479149
It's easy to see why these patterns occur if you try them using log division.
0
 
LVL 18

Expert Comment

by:JR2003
ID: 12479152
It's easy to see why these patterns occur if you try them using LONG division.
0
 
LVL 22

Author Comment

by:grg99
ID: 12486123
some primes <<p>> have the longest repeating substring <<p - 1>>, being <<7>> the smallest one
<<1 / 7 = 0,14285714285714285714285714285714...>>

IIRC:
What's even more interesting, TWO sevenths is: .285714285714....., FOUR sevents is .57142857....

0
 
LVL 31

Accepted Solution

by:
GwynforWeb earned 2000 total points
ID: 12511230
Multiply 37,037 by any single number (1-9), then multiply that number by 3. Every digit in the answer will be the same as that first single number. (this is failry easy to work out but still cute)
0
 
LVL 31

Expert Comment

by:GwynforWeb
ID: 12528243
Thanks for the points :-)
0

Featured Post

[Webinar] Cloud and Mobile-First Strategy

Maybe you’ve fully adopted the cloud since the beginning. Or maybe you started with on-prem resources but are pursuing a “cloud and mobile first” strategy. Getting to that end state has its challenges. Discover how to build out a 100% cloud and mobile IT strategy in this webinar.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
Aerodynamic noise is the cause of the majority of the noise produced by helicopters. The inordinate amount of noise helicopters produce is a major problem in the both a military and civilian setting. To remedy this problem the use of an aerogel coat…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
Suggested Courses

839 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question