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0.9999... = 1

lets try:

x=4.4444.....
10x=44.4444.....
10x-x=44.4444....-4.4444....
9x=40
x=4.4444.....

dosnt give complete number as above
 
People use this technique to convert this kind of decimal numbers with repeats(forgot what it's called) into fractions.

Let x = 0.9999 ....
then 10x = 9.9999 ...
with 10x - x = 9.9999 ... - 0.9999 ....
9x = 9
x = 1/1 (or 1 if you simplifie it)

Because you get the answer as 1, you won't notice it. This is a special one actually.

x = 4.4444.....
10x = 44.4444.....
10x - x= 44.4444....-4.4444....
9x = 40
x = 40/9 (don't use calculator)

Let x = 0.234234234...
then 1000x = 234.234234...
1000x - x = 234.234.234... - 0.234234...
999x = 234
x = 26/111

Thus, the fraction is a more accurate number.
 
Last edited:
Originally posted by Demigod
shouldnt 10x - x be the same as 9x?

0.9999 x 9 = 8.9991
9.9999 - 0.9999 = 9.

didnt work.
Click to expand...

oops. wait, I see where I made my mistake.

x = 0.9999
10x = 9.999 (there's one less nine after you move the decimal)
10x - x = 8.9991
9x=8.9991
x=0.9999
 
it was 9.99999999999999999999999999999999, not 9.9999,
9.9999...... the dots to show infinity :)
 
We're taught to use lines, called "bar".
          _
Like: 0.9
 
i already know that the eps. stand for infinite 9's behind it. im just saying...maybe when you move the decimal over, there's one less nine, regardless if its a repeating decimal or not.
might not make sense but it works.
 
Originally posted by Demigod

i already know that the eps. stand for infinite 9's behind it. im just saying...maybe when you move the decimal over, there's one less nine, regardless if its a repeating decimal or not.
might not make sense but it works.
Click to expand...
And I ask you...what is infinity minus one?

Originally posted by LeX
We're taught to use lines, called "bar".
_
Like: 0.9
Click to expand...
It's called a repetend bar. It's pretty much a big no-no in higher levels of math.

As Weirds pointed out, people use this technique to convert infintely repeating decimals into fractions. We know that 0.999... is a rational number, and therefore it must have a corresponding fraction. That particular fraction is 1/1, or in simplified form: 1.
 
I already told you, it wont make sense.

But then, how do multiply infinite by 10, subtract infinite, and then get it to equal 1. A number cant be the same as another number. .9.... is not 1.
 
Originally posted by Demigod

But then, how do multiply infinite by 10, subtract infinite, and then get it to equal 1. A number cant be the same as another number. .9.... is not 1.
Click to expand...
You are not multiplying infinity by 10. Rather, you are multiplying by a rational number with infinitely many decimal places.

Another proof that .999... = 1: two numbers are distinct if there are infinitely many numbers between them. There are no values between .999... and 1; therefore, the two numbers are the same.
 
Just want to add to this yet another proof. .9999... = 1. It does. I asked my math professor, and it does. Well, he showed me this whole long calculus operation on why and how... I don't remember it, but .999...=1. Think about it:

1/3 =.33333333.... = 1/3
2/3 =.66666666.... = 2/3
3/3 =.99999999.... = 1
 
Originally posted by shizzle
Just want to add to this yet another proof. .9999... = 1. It does. I asked my math professor, and it does. Well, he showed me this whole long calculus operation on why and how... I don't remember it, but .999...=1. Think about it:

1/3 =.33333333.... = 1/3
2/3 =.66666666.... = 2/3
3/3 =.99999999.... = 1
Click to expand...

Ok. That kinda made a little more sense for me now. It's still wierd though. I guess we'll just leave it at that.

.9999....=1
 
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