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9/22/2017 12:11:25 AM
Posted: 2/21/2006 4:29:48 PM EDT
S=t1=0.45= 0.45= 5
--- ----- ---- --
1-r 1-0.01 0.99 11

I know that if you divide the 0.45 and the 0.99 by .09 you get the 5 over 11 but why do you divide by the .09? How do you know to divide by .09?

Thanks
TrojanFan
Link Posted: 2/21/2006 4:31:16 PM EDT
[Last Edit: 2/21/2006 4:31:59 PM EDT by Red_Beard]


How do I turn an irrational number into a fraction without using a calculator?


you don't
Link Posted: 2/21/2006 4:31:21 PM EDT
Your making my brain hurt! Ask this again in the morning.
Link Posted: 2/21/2006 4:33:35 PM EDT

Originally Posted By Red_Beard:

How do I turn an irrational number into a fraction without using a calculator?



Try to calmly reason with it. Be firm but remain calm.
Link Posted: 2/21/2006 4:41:17 PM EDT
OK although these are fairly good answers for going on 2000 hrs (8pm) after a 3 day weekend BUT since this is for my son who has a quiz in the morning on this I will need a little more mathmatical input and less philosophical input, although he is tempted to use the "misterc" reply and see if he gets bonus points.
Link Posted: 2/21/2006 4:45:11 PM EDT

Originally Posted By MisterC:


Try to calmly reason with it. Be firm but remain calm.




LOL
Link Posted: 2/21/2006 4:48:28 PM EDT
Come on where are all the think tankmath wizard nasa types when you need them?!?!?
In the 8 years or so we have been on this board we have never posted a question that the members here couldn't answer, so I know that this wont be the first.
Link Posted: 2/21/2006 4:53:23 PM EDT
[Last Edit: 2/21/2006 4:56:01 PM EDT by clement]
Well I think your problem is by definition an IRrational number is one that cannot be expressed as a quotient of two numbers (i.e. a fraction)

I'd help ya but its been years since I did what you actually want help with and I forgot it all
Link Posted: 2/21/2006 4:55:08 PM EDT
45/100
Link Posted: 2/21/2006 4:55:34 PM EDT
What irrational number are you trying to put into a calculator?

e

π

sqrt(2)
Link Posted: 2/21/2006 4:56:17 PM EDT
[Last Edit: 2/21/2006 4:57:07 PM EDT by NwG]
S=t1=0.45= 0.45= 5
--- ----- ---- -- = 8/7?
1-r 1-0.01 0.99 11

sorry had to
Link Posted: 2/21/2006 4:56:18 PM EDT
[Last Edit: 2/21/2006 4:58:47 PM EDT by jblachly]

Originally Posted By TrojanFan:
OK although these are fairly good answers for going on 2000 hrs (8pm) after a 3 day weekend BUT since this is for my son who has a quiz in the morning on this I will need a little more mathmatical input and less philosophical input, although he is tempted to use the "misterc" reply and see if he gets bonus points.




Come on where are all the think tankmath wizard nasa types when you need them?!?!?
In the 8 years or so we have been on this board we have never posted a question that the members here couldn't answer, so I know that this wont be the first.



The very first reply to the thread was your answer, whether you choose to believe it or not.

I will summarize what another poster said as well.

The definition of an irrational number is one that cannot be turned into a fraction of two integers.



Link Posted: 2/21/2006 5:00:45 PM EDT
I would say... hmm... how do u make an irrational # into a fraction?
Very Carefully!
lol
Link Posted: 2/21/2006 5:02:26 PM EDT
What these guys said ... You can't do it. By definition an irrational number can not be made into a fraction (rational number).
Link Posted: 2/21/2006 5:04:24 PM EDT
All of the above responses are correct. By definition you cannot convert an irrational number into a fraction. But I think what you are really asking is how to turn a repeating decimal into a fraction. For that answer, go look here:

Need to convert a repeating decimal to a fraction?

Link Posted: 2/21/2006 5:04:58 PM EDT
It is a repeating decimal.
In the equation I first listed, that is the whole thing, we just dont know how they went from the next to last step to the final answer.
I mean we know they divided the numerator and denomenator by .09 but why???
Link Posted: 2/21/2006 5:07:01 PM EDT

Originally Posted By TrojanFan:
It is a repeating decimal.
In the equation I first listed, that is the whole thing, we just dont know how they went from the next to last step to the final answer.
I mean we know they divided the numerator and denomenator by .09 but why???


See my post just above yours.
Link Posted: 2/21/2006 5:07:41 PM EDT
[Last Edit: 2/21/2006 5:10:53 PM EDT by JasonD]

Originally Posted By TrojanFan:
S=t1=0.45= 0.45= 5
--- ----- ---- --
1-r 1-0.01 0.99 11

I know that if you divide the 0.45 and the 0.99 by .09 you get the 5 over 11 but why do you divide by the .09? How do you know to divide by .09?

Thanks
TrojanFan



If I am reading correctly, you have the equation S = (T1)/ (1 - R) you then substituted T1=0.45 and R = 0.01 and ended up with the fraction 0.45/0.99. And your question is how to reduce it.

The answer to that is to treat it like 45/99 (multiply by 100/100), and then factor a 9 out of the numerator and denominator to get to 5/11
Link Posted: 2/21/2006 5:11:00 PM EDT

Originally Posted By fatk1d:
What these guys said ... You can't do it. By definition an irrational number can not be made into a fraction (rational number).



This is entirely true.

I would like to note however that Irrational Numbers fall into 2 categories: (Algebraic Irrational Numbers - such as the square root of 2, and Transcendental Irrational Numbers such as Pi or e.)

Having acknowledged that it is impossible to Express single Irrational Number as a Fraction. You can Transform an Irrational Number and map it to the Rational Numbers through multiplication.

For example Sqrt(2) * Sqrt(2) = 2 (2 can be expressed as 2/1, therefore it is a Rational Number)

Similarly Pi * 2/(3*Pi) = 2/3

{Rational Numbers} UNION {Irrational Numbers} = Real Number Set
Link Posted: 2/21/2006 5:13:10 PM EDT

Originally Posted By Bostonterrier97:

Originally Posted By fatk1d:
What these guys said ... You can't do it. By definition an irrational number can not be made into a fraction (rational number).



This is entirely true.

I would like to note however that Irrational Numbers fall into 2 categories: (Algebraic Irrational Numbers - such as the square root of 2, and Transcendental Irrational Numbers such as Pi or e.)

Having acknowledged that it is impossible to Express single Irrational Number as a Fraction. You can Transform an Irrational Number and map it to the Rational Numbers through multiplication.

For example Sqrt(2) * Sqrt(2) = 2 (2 can be expressed as 2/1, therefore it is a Rational Number)

Similarly Pi * 2/(3*Pi) = 2/3

{Rational Numbers} UNION {Irrational Numbers} = Real Number Set



Can you explain why e^(pi*i) = -1 smarty pants?
Link Posted: 2/21/2006 5:14:52 PM EDT

Originally Posted By MisterC:

Originally Posted By Red_Beard:

How do I turn an irrational number into a fraction without using a calculator?



Try to calmly reason with it. Be firm but remain calm.



You know...George Cantor tried to reason with a bunch of Irrational Numbers...and look where it got him! He ended up in an Insane Asylum! Just because this group of Irrational Numbers convinced him that even there were an INFINITE Number of Rational Numbers and an INFINITE Number of Irrational Numbers...there were always MORE Irrational Numbers than Rational Numbers. Even though both were Infinite Sets.

So you see...it is little wonder that poor Mr. Cantor ended up completely Irrational with his Diagonalization Arguement!

Link Posted: 2/21/2006 5:15:10 PM EDT

Originally Posted By Bostonterrier97:
Having acknowledged that it is impossible to Express single Irrational Number as a Fraction. You can Transform an Irrational Number and map it to the Rational Numbers through multiplication.

For example Sqrt(2) * Sqrt(2) = 2 (2 can be expressed as 2/1, therefore it is a Rational Number)

Similarly Pi * 2/(3*Pi) = 2/3



That's some pretty wacky stuff.

What's the point?

Link Posted: 2/21/2006 5:15:31 PM EDT
Thank you, that site was exactly what we were looking for.
Your help is greatly appreciated.
Once again the ARFCOM Think Tank comes through!!!
Thanks

TrojanFan and TrojanFan Jr.
Link Posted: 2/21/2006 5:17:26 PM EDT

Originally Posted By clement:

Originally Posted By Bostonterrier97:

Originally Posted By fatk1d:
What these guys said ... You can't do it. By definition an irrational number can not be made into a fraction (rational number).



This is entirely true.

I would like to note however that Irrational Numbers fall into 2 categories: (Algebraic Irrational Numbers - such as the square root of 2, and Transcendental Irrational Numbers such as Pi or e.)

Having acknowledged that it is impossible to Express single Irrational Number as a Fraction. You can Transform an Irrational Number and map it to the Rational Numbers through multiplication.

For example Sqrt(2) * Sqrt(2) = 2 (2 can be expressed as 2/1, therefore it is a Rational Number)

Similarly Pi * 2/(3*Pi) = 2/3

{Rational Numbers} UNION {Irrational Numbers} = Real Number Set



Can you explain why e^(pi*i) = -1 smarty pants?



Trivial!

e(pheta*i) = Cos(pheta) + i*sin(pheta)
Let pheta = Pi and you get sin(Pi) = 0 and Cos((Pi) = -1

Therefore e(pheta*i) = Cos(pheta) + i*sin(pheta) = -1 + i*0 = -1

Link Posted: 2/21/2006 5:18:05 PM EDT
[Last Edit: 2/21/2006 5:18:55 PM EDT by JasonD]

Originally Posted By clement:

Originally Posted By Bostonterrier97:

Originally Posted By fatk1d:
What these guys said ... You can't do it. By definition an irrational number can not be made into a fraction (rational number).



This is entirely true.

I would like to note however that Irrational Numbers fall into 2 categories: (Algebraic Irrational Numbers - such as the square root of 2, and Transcendental Irrational Numbers such as Pi or e.)

Having acknowledged that it is impossible to Express single Irrational Number as a Fraction. You can Transform an Irrational Number and map it to the Rational Numbers through multiplication.

For example Sqrt(2) * Sqrt(2) = 2 (2 can be expressed as 2/1, therefore it is a Rational Number)

Similarly Pi * 2/(3*Pi) = 2/3

{Rational Numbers} UNION {Irrational Numbers} = Real Number Set



Can you explain why e^(pi*i) = -1 smarty pants?




according to Euler e^(pi*i) = cos (pi) + i*sin(pi)

sin (pi) = 0 cos(pi) = -1 in case he doesnt get it


bah beat me to it
Link Posted: 2/21/2006 5:21:29 PM EDT

Originally Posted By Red_Beard:

Originally Posted By Bostonterrier97:
Having acknowledged that it is impossible to Express single Irrational Number as a Fraction. You can Transform an Irrational Number and map it to the Rational Numbers through multiplication.

For example Sqrt(2) * Sqrt(2) = 2 (2 can be expressed as 2/1, therefore it is a Rational Number)

Similarly Pi * 2/(3*Pi) = 2/3



That's some pretty wacky stuff.

What's the point?




Not wacky at all, merely pointing out the difference between expressing a number versus performing a function (or mapping or transformation) on a number

or in this case a set of numbers such as the {cube root of any positive rational number} can be mapped to the set of all positive Rational Numbers through the function of cubing the {set of cube roots of any positive rational number}
Link Posted: 2/21/2006 5:22:55 PM EDT

Originally Posted By JasonD:

Originally Posted By clement:

Originally Posted By Bostonterrier97:

Originally Posted By fatk1d:
What these guys said ... You can't do it. By definition an irrational number can not be made into a fraction (rational number).



This is entirely true.

I would like to note however that Irrational Numbers fall into 2 categories: (Algebraic Irrational Numbers - such as the square root of 2, and Transcendental Irrational Numbers such as Pi or e.)

Having acknowledged that it is impossible to Express single Irrational Number as a Fraction. You can Transform an Irrational Number and map it to the Rational Numbers through multiplication.

For example Sqrt(2) * Sqrt(2) = 2 (2 can be expressed as 2/1, therefore it is a Rational Number)

Similarly Pi * 2/(3*Pi) = 2/3

{Rational Numbers} UNION {Irrational Numbers} = Real Number Set



Can you explain why e^(pi*i) = -1 smarty pants?




according to Euler e^(pi*i) = cos (pi) + i*sin(pi)

sin (pi) = 0 cos(pi) = -1 in case he doesnt get it


bah beat me to it



Euler was BRILLIANT. Imagine churning out enough scientific papers to fill 80 volumes, and doing quite a bit of it BLIND!
Link Posted: 2/21/2006 5:24:58 PM EDT
[Last Edit: 2/21/2006 5:34:25 PM EDT by clement]

Originally Posted By Bostonterrier97:

Originally Posted By MisterC:

Originally Posted By Red_Beard:

How do I turn an irrational number into a fraction without using a calculator?



Try to calmly reason with it. Be firm but remain calm.



You know...George Cantor tried to reason with a bunch of Irrational Numbers...and look where it got him! He ended up in an Insane Asylum! Just because this group of Irrational Numbers convinced him that even there were an INFINITE Number of Rational Numbers and an INFINITE Number of Irrational Numbers...there were always MORE Irrational Numbers than Rational Numbers. Even though both were Infinite Sets.

So you see...it is little wonder that poor Mr. Cantor ended up completely Irrational with his Diagonalization Arguement!




Doesn't that have to do with how you can map the set of all positive and negative integers to only the set of all positive integers? I remember all that stuff

Like how there are still more irrational numbers between 0 and 1 then there are rational numbers
Link Posted: 2/21/2006 5:28:53 PM EDT
[Last Edit: 2/21/2006 5:30:42 PM EDT by dugedug]

Originally Posted By clement:

Can you explain why e^(pi*i) = -1 smarty pants?


Eulers...

im too slow today
Link Posted: 2/21/2006 5:31:16 PM EDT
Although I enjoy complex problems and discusion points my 17 y/o son is in classes like...
Advanced Placement Calc/Trig combo course
Advanced Placement Physics
Advanced Placement CompScience Programming
Advanced Placement World lit
And others
He also finds the time to play QB on offense and FS on defense
He also has a job
He can play all 80's metal guitar music
And is an all around good non gang banger, non drug user, non rap kind of kid who also happens to be able to shoot 10 out of 10 at 100m on a 3 inch shoot n see and 6 or 7 out of 10 at 200m with a Colt 20" AR.
I'm a proud papa and I have 3 other younger boys too.
So i figure if I bring them all up right I will be able to retire one day and never have to worry about them taking care of themselves.
Link Posted: 2/21/2006 5:33:10 PM EDT

Originally Posted By TrojanFan:
Although I enjoy complex problems and discusion points my 17 y/o son is in classes like...
Advanced Placement Calc/Trig combo course
Advanced Placement Physics
Advanced Placement CompScience Programming




Cool tell him to stick with the math when he gets to college and he'll soon be messing with problems like that infinite numbers/cardinality bullshit above.

Link Posted: 2/21/2006 5:33:54 PM EDT

Originally Posted By JasonD:
e^(pi*i) = cos (pi) + i*sin(pi)




Can you explain that one?

Link Posted: 2/21/2006 5:35:02 PM EDT
Nah, it will be Laplace, Fourier Transforms, Transform equations and Tunneling if he plays his cards right.
Link Posted: 2/21/2006 5:35:49 PM EDT

Originally Posted By Red_Beard:

Originally Posted By JasonD:
e^(pi*i) = cos (pi) + i*sin(pi)




Can you explain that one?



A trig identity.
Link Posted: 2/21/2006 5:37:44 PM EDT
Cantor developed a neat theary of infinities. Denumerable infinities can be paired with the intigers (called aleph-1). Non-denumerable infinites are one level higher (called aleph-2). Like the example posted of intigers being an infinite set, but there are an infinity of rational numbers between any two integers.
Some of the answers get pretty weird. Like an infinite checkerboard still being denumerable, so aleph-1 squared remains denumberable.
His theories put many conepts involving limits onto a solid footing.
Link Posted: 2/21/2006 5:41:44 PM EDT
He likes to study things like string theory, black holes and such too.
We is considering some sort of comp sci engineering degree.
He likes programming and he likes designing and inventing things and retrofitting things to work better.
Link Posted: 2/21/2006 5:44:09 PM EDT
Link Posted: 2/21/2006 5:46:18 PM EDT
He has been offered to go to DC for a class on homeland defense dealing with comp sci security stuff and DOD think tank stuff, but I have to come upwiththe 5K for him to go.
He is going to prob go to TU for his 4 yr degree than MIT he hopes for a masters but he is applying to MIT and seeing if he can do all 6 yrs at MIT on a full scholarship.
He told his mom and I he wanted to go to MIT when he ws 5 yrs old in kindergartne and doing talented and gifted classes with 5th graders. He read a pop sci mag with an MIT article and he has been hooked since.
Link Posted: 2/21/2006 5:47:41 PM EDT
Chuck Norris once ran into a irrational number while doing his taxes. He pondered this a while, then roundhouse kicked it so hard it turned into an integer. We now know that number as 87.
Link Posted: 2/21/2006 5:48:09 PM EDT
MRW to answer your "Why" question...

So that we can not only know what gun Al Pacino used in Heat, but WHY he used that weapon and how it will work on zombies in space with a 1/7 twist.
Link Posted: 2/21/2006 5:49:03 PM EDT

Originally Posted By TrojanFan:
We is considering some sort of comp sci engineering degree.
... things to work better.



That's like saying Military Intelligence.

Physics is were your going to get the most string theory. I had a bit of string in EE but alot more about tunnelling and such in nanotech/materials classes (tunnelling is far more useful right now i.e. transistors).

stuff like this:
http://www.aip.org/pnu/1998/split/pnu357-1.htm
Link Posted: 2/21/2006 5:49:07 PM EDT
[Last Edit: 2/22/2006 3:04:09 AM EDT by MRW]
Link Posted: 2/21/2006 5:49:53 PM EDT

Originally Posted By MRW:
yada yada yada... all this is fun and games

but what does it all MEAN?

There is order and rationality in the universe and man is somehow fashoned to discover and understand it

WHY?

For what purpose?



Because we can.
Link Posted: 2/21/2006 6:02:44 PM EDT

Originally Posted By Red_Beard:

Originally Posted By JasonD:
e^(pi*i) = cos (pi) + i*sin(pi)




Can you explain that one?




Not without copying it out of my system dynamics text no.

Link Posted: 2/21/2006 6:21:43 PM EDT

Originally Posted By Red_Beard:

Originally Posted By TrojanFan:
Although I enjoy complex problems and discusion points my 17 y/o son is in classes like...
Advanced Placement Calc/Trig combo course
Advanced Placement Physics
Advanced Placement CompScience Programming




Cool tell him to stick with the math when he gets to college and he'll soon be messing with problems like that infinite numbers/cardinality bullshit above.




Gauss once said that Mathematics is the Queen of Sciences, and Number theory is the Queen of Mathematics.

Link Posted: 2/21/2006 6:25:24 PM EDT
[Last Edit: 2/21/2006 6:26:15 PM EDT by Bostonterrier97]

Originally Posted By JasonD:

Originally Posted By Red_Beard:

Originally Posted By JasonD:
e^(pi*i) = cos (pi) + i*sin(pi)




Can you explain that one?




Not without copying it out of my system dynamics text no.




Easy, perform a taylor series expansion on e^(x*i)
Then decompose your series expansion in the form of (yada yada yada) + (why why why)*i

Next perform taylor series exapansion on both Cos(x) and Sin(x)

Notice anything?

Link Posted: 2/21/2006 6:33:44 PM EDT
[qoute]How do I turn an irrational number woman into a fraction without using a calculator?[/qoute]
There fixed it

And with an AXE

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