A Math problem

[Alaskanbullworm]

You know that 1/3 is.3 repeating and 2/3 is .6 repeating , so if you add the decimals it's .9 repeating . But, 1/3 plus 2/3 is one . So, does this mean .9 repeating is equal to 1 ? I know some of you will say just round it up.

[Danielle]

No! Not math! :eek:

Unfortunately, my grade for math is currently underwater, so I can't help you. Ask some of the people who actually know how to factor quadratic equations. :rolleyes: Definently not my field....

[Alaskanbullworm]

Actually, I'm very good in MATH, but this one just baffles me.

[optimal321]

Actually... yes it does. We learned about this in school to convert repeating decimals to fractions. First, we start w/ :

.99999999999999...

Set that equal to x:

x = .999999999.....

Multiply by ten:

10x = 9.9999999........

Now we have two equations. We subtract an x from both sides, (which is equivalent to .99999999999.... remember) and get:

9x = 9

x = 9/9

.999999999999........... = 1

Tada!!! Or it was something like that :rolleyes:

Questions class? ;)

[Sumi_Masen]

you would think that currently being in algebra would be of some use.

[optimal321]

I guess it's kinda like a limit problem. It approaches one, and gets closer and closer w/ every digit you add, but you'll never quite get there. But for the mathematician's purposes (or at least what my teacher said! :D ) my above proof shows that for calculation purposes, .9999999999999......... does equal one.

[pencilsharp]

Ignoring the fact that 1/3 and 2/3 translate into repeating decimals that never quite equal the original (which explains the discrepancy between the sums), you need to remember that math is NOT an exact science. In fact, like the other sciences, math is pure theory.

It's an incomplete theory to boot. There are some things that just can't be figured, like pi, the square root of 2, and division by zero. Even something simple like '2+2=4' is open to debate. (What exactly is 4, anyway?)

So, rack that one up to that old mathemagical demon, impreciseness.

Or am I waaay overanswering this? :confused:

[Naraht]

if you want to get really technical 1/9 == .111111111111111111111
2/9 = .2222222222222222222222
3/9 == 1/3 = .333333333333333333333333333
4/9 = .4444444444444444444444444444
5/9 = .555555555555555555555555
need I go on?

[JustJack]

All math is just one big lie....none of it actually works!! AH HAHAHAHAAHAHA!!!

"Anti-Math: 3 years, and running...backwards..."

[Jedi Knight]

I don't know about any of the other proofs above, but the simple way that I always though about it was , what happens if you subtract .9(repeating) from 1?

1.0000000000
-0.9999999999
?

Basically, you know it's going to be 0.0000...with a 1 WAY at the end, but where do you put that 1? Since it goes forever, you don't put it anywhere. 1 - .9(repeating) = 0, so they're the same number.

[pencilsharp]

Jedi Knight wrote...
where do you put that 1? Since it goes forever, you don't put it anywhere. 1 - .9(repeating) = 0, so they're the same number. Au contraire, mon frere. True, the answer repeats forever, but it is NOT equal to zero. Therefore...

1 - 0.999(etc) is not equal to 0.000(etc)01!
Why? Because the latter number has an END. The difference you're talking about does not.

It is an imaginary number. It doesn't truly exist. And that just drives mathematicians up the wall.

Just one more reason to give up math and take up knitting.

[Alaskanbullworm]

It's almost like asking what's the square root of -1. Well, the square root of -4 is 2i where i isn't a real number. Weird huh?

[Twilight]

Originally posted by optimal321
Actually... yes it does. We learned about this in school to convert repeating decimals to fractions. First, we start w/ :

.99999999999999...

Set that equal to x:

x = .999999999.....

Multiply by ten:

10x = 9.9999999........

Now we have two equations. We subtract an x from both sides, (which is equivalent to .99999999999.... remember) and get:

9x = 9

x = 9/9

.999999999999........... = 1

Tada!!! Or it was something like that :rolleyes:

Questions class? ;)
Cool. I remember that from my high school days. Here's a riddle that relates to all this fraction confusion. :p

A man has 3 sons and 17 horses. He dies and stated in his will that he wants his horses divided between his sons: the oldest gets 1/2 of the horses, the 2nd eldest gets 1/3, and the youngest gets 1/9. The three sons are confused about how many horses they each get, and they couldn't ask their father since he's dead. But their mother had a solution and figured it out. How many horses does each son get??

[Jedi Knight]

Originally posted by pencilsharp

1 - 0.999(etc) is not equal to 0.000(etc)01!
Why? Because the latter number has an END. The difference you're talking about does not.



Close enough. By the way, imaginary numbers are square roots of negative numbers. And mathemeticians aren't driven up the wall by this problem, because .9(repeating) is deemed to equal 1, even if it doesn't technically equal one. Like I said, close enough.



Originally posted by Twilight

A man has 3 sons and 17 horses. He dies and stated in his will that he wants his horses divided between his sons: the oldest gets 1/2 of the horses, the 2nd eldest gets 1/3, and the youngest gets 1/9. The three sons are confused about how many horses they each get, and they couldn't ask their father since he's dead. But their mother had a solution and figured it out. How many horses does each son get??



Easy, she borrowed one horse from someone, so now the total is 18. The oldest gets 9 horses, the 2nd eldest gets 6 horses, and the youngest gets 2 horses. 9+6+2 = 17.

The remaining horse goes back to whoever it was borrowed from.
(This is actually more of a riddle, not a math problem)

[optimal321]

Here's a proof my Algebra I teacher taught us, showing that zero equals one.

0 = 1

Subtractc 1/2:

-1/2 = 1/2

Square both sides:

1/4 = 1/4

There ya go! :p

[Naraht]

Originally posted by optimal321
Here's a proof my Algebra I teacher taught us, showing that zero equals one.

0 = 1

Subtractc 1/2:

-1/2 = 1/2

Square both sides:

1/4 = 1/4

There ya go! :p

ummm, no...you can't start with 0=1....cause it doesn't.

yes, both negative 1/2 and 1/2 squared = 1/4...

-2 and 2 squared equal 4....doesn't mean they're the same number...

that's why you'll learn that the square root of 4 is +or- 2.....

[DR. BELCH]

--of the paradox of halves: if a guy and a girl stand, say, ten feet apart, and then one comes half that distance to the other (5 ft), then half that distance (2.5 ft), then half that, they theoretically will never meet, because there will always be a half of x to travel.

Then there's my favorite problem, the four nines. Using any rule of math--add, subtract, divide, multiply--use four nines to equal sums from 1 to 20. To solve this I developed what I call the uberroot--that is, if you break a number down enough times into its square roots, it will eventually equal one.

[Spaceman Spiff]

Hmm, I'll give that a try. Sounds like you want to stick to algebra, though that "uberroot" is stretching it. :D

(9/9)/(9/9)=1
9/9+9/9=2
(9+9+9)/9=3
sqrt(sqrt(9*9))+9/9=4
9-sqrt(9)-9/9=5
(9+9)/sqrt(sqrt(9*9))=6
9-(9+9)/9=7
((9*9)-9)/9=8
(9-9)/9+9=9
((9*9)+9)/9=10
(9+9)/9+9=11
9+sqrt(9)+9-9=12
9+sqrt(9)+9/9=13

9+9-sqrt(sqrt(9*9)=15

(9+9)-(9/9)=17
9-9+9+9=18
(9+9)+(9/9)=19


That's all I can come up with. Though I do wonder if you can do it without the squre roots

[Sumi_Masen]

Oi! All this math.......ugh! 'Tis so confusing!

[Joe Tully]

Originally posted by Twilight

Cool. I remember that from my high school days. Here's a riddle that relates to all this fraction confusion. :p

A man has 3 sons and 17 horses. He dies and stated in his will that he wants his horses divided between his sons: the oldest gets 1/2 of the horses, the 2nd eldest gets 1/3, and the youngest gets 1/9. The three sons are confused about how many horses they each get, and they couldn't ask their father since he's dead. But their mother had a solution and figured it out. How many horses does each son get??

Oh boy, I could make a million guesses on that one.

But I'll say chop up the horses so you can distribute them equally according to the fractions, and throw away the rest. Not because I think that it's the answer you're looking for, just because it's a possible answer that's incredibly gross. :p

[Elven Moon]

*holds head and screams* Math! My absolute worst subject. I've struggled with math since I was young enough to breathe! *wanders away, a cloud over her head* Math... augh... numbers...

[optimal321]

Originally posted by naraht


ummm, no...you can't start with 0=1....cause it doesn't.

yes, both negative 1/2 and 1/2 squared = 1/4...

-2 and 2 squared equal 4....doesn't mean they're the same number...

that's why you'll learn that the square root of 4 is +or- 2.....

Well, i know that :rolleyes: . I don't really belive that 0 = 1. It was just a fun little thing my teacher showed us that i thought i'd share. Of course it doesn't work right. My legal proof was the 1 = .999999999...

And i know the whole +- thing after you take a square root.