Solved

Decimal->Geometric Series

Posted on 2006-07-23
6
570 Views
Last Modified: 2012-08-13
Hi. I'm attempting to convert a decimal to a geometric series of the form ar^n. Does anybody know of any neat little ways to go about doing this? I haven't been able to find anything all that useful on the web yet.

i.e.
4.1666666(6)
.45114141414(14)

Thanks.
0
Comment
Question by:NorCal19
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 3
  • 2
6 Comments
 
LVL 37

Expert Comment

by:Harisha M G
ID: 17163438
Hi, I don't really understand your question. Can you give an example ?

Let x = 4.16666...
10x = 41.66666...

Subtracting 1 from 2,
9x = 37.5

So, x = 75/18

Hence, any recurring fraction can be put in the form of a fraction.

What do you mean by form of ar^n ?

For your second fraction,

Let x =      .4511414...
100 x = 45.11414...

So, 99x = 44.663

x = 44663/99000

---
Harish
0
 
LVL 27

Expert Comment

by:d-glitch
ID: 17163440
I don't know about geometric series.

Ususally what you want to do with repeating decimals is convert them to fractions:

    10*X = 41.66666
         X  =  4.16666
---------------------------
      9*X = 37.50000       ==>   X  =  37.5/9  =  375/90  =  75/18  =  25/6


For the second one you would have to do

  100*Y = 45.1141414
         Y  =  0.4511414
0
 
LVL 37

Accepted Solution

by:
Harisha M G earned 250 total points
ID: 17163485
Ah well.. I do get an idea of what you might be asking now :)

4.16666

= 4.1 + 0.06 + 0.006 + 0.0006 + ...
= 4.1 + Geometric series(a = 0.06, r = 0.1)

For the second,

0.4511414

= .451 + 0.00014 + 0.0000014 + ...
= .451 + Geometric series(a = 0.00014, r = 0.01)
0
Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

 

Author Comment

by:NorCal19
ID: 17163491
Hi, I don't really understand your question. Can you give an example ?:

Say for example I wanted to express .080808(08) as the ratio of two integers:

.080808... = 8/(10^2) + 8/(10^4) + 8/(10^6) + 8/(10^8) + ...

sooo we could write that as: Summation(n = 0 -> infinity) (8/(10^2)) (1/(10^2))^n

(Sorry, I don't know how to do summation notation correctly in text. (see above))

So here we have the form ar^n with a = (8/(10^2)) and r = (1/(10^2)). I guess you can use this to find the sum which would be (a/1-r). Anyway, hopefully that example clarified it a bit.

So I guess I'm just trying to apply this same idea to these other two examples whose repeating parts don't start immediately to the right of the decimal as this example does.

Thanks!
0
 

Author Comment

by:NorCal19
ID: 17163508
ahhhh ok I think I've been beating my head against a wall for no reason:

I had something almost identical to this: .451 + Geometric series(a = 0.00014, r = 0.01)

But I thought that the .451 part had to be somehow in the series (which was not making sense to me)...

so I guess my series for the second example would be:

.451 + Summation(n=0,infinity)(14/10^5)(1/.01)^n

?

0
 

Author Comment

by:NorCal19
ID: 17163522
Ok my previous post was wrong:

The series is:

.451 + Summ(n=0,infinity) (14/10^5) (1/100)^n

Thanks Harish! :)
0

Featured Post

Independent Software Vendors: We Want Your Opinion

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

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

This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
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…

695 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