This introductory course to Windows 7 environment will teach you about working with the Windows operating system. You will learn about basic functions including start menu; the desktop; managing files, folders, and libraries.

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.

i.e.

4.1666666(6)

.45114141414(14)

Thanks.

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

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

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!

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

?

Question has a verified solution.

Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.

Have a better answer? Share it in a comment.

All Courses

From novice to tech pro — start learning today.

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)