Is 0.99999... repeated equal to one?

yes

The best real proof is:
x = 0.9999999.....
10x = 9.999999......
10x - x = 9.999999...... - 0.9999999.......
9x = 9
x = 1

Basing things on 1/3= 0.33333333333... isnt really a proof

Heres an example (not a proof)

1/9 = 0.1111111........
2/9 = 0.2222222222222222222........
3/9 = 1/3 = 0.33333333333.....
4/9 = 0.444444444444..........
5/9 = 0.555555555..........
6/9 = 2/3 = 0.666666666666......
7/9 = 0.777777777777777.....
8/9 = 0.88888888........
9/9 = 0.9999999999999999...
(but you know 9/9 = 1 also!)

Do not believe those who tell you they are close enough to be the same, its not like that. They ARE the same. They are equal - its all to do with the maths of infinity, absolutely fascinating, I love it!

Absolutely sure! They are equal and not just close enough to say they are equal.

They are one and the same

Yes

0.999999....
= 9/10 + 9/100 + 9/1000 + ....
This is an infinite geometric series.
S = a/(1-r)
= (9/10) / (1 - 1/10)
= (9/10) / (9/10)
= 1

-----------------------------

x = 0.9999999.....
10x = 9.999999......
10x - x = 9.999999...... - 0.9999999.......
9x = 9
x = 1

Answer: 0.99999...repeated is equal to 1.

Yes.

N = 0.999...

10N = 9.999...

Multiply the first equation by -1 and add it to the second equation.

10N + -N = 9.999... + -0.999...

9N = 9

N = 1

0.999... = 1

Yes!!

There are many proofs / demonstrations around...

x = 1/3 = .33333..... ( I don't think anyone disagrees with this!)So 3x = 3/3 = 1 = .99999999999999....
3 * (1/3) = 1
3 * .3333.... = .9999999..... = 1

or, let x = .99999999....
10 x = 9.999999999....
10x - x = 9x
and 9.99999.... - .99999 = 9.0
so 9x = 9, or x = 1

Don't let the naysayers get you down!

As other people have said, this isn't just an approximation for convenience, it is an exact value.

0.999999...... = 1 ?

Let's see is 0.999999...... = 1 or not:

x = 0.999999......

10x = 9.999999......
10x - x = 9.999999...... - 0.999999......
9x = 9
x = 9/9
x = 1

∴ 0.999999...... = 1

There's a couple classic proofs (actually more like demonstrations - they don't really qualify as proofs).

first one:
1/3 = 0.33333....
3 * 1/3 = 1

substitute for 1/3:
3 * 0.333333... = 0.99999...

substitute back:
3 * 1/3 = 0.99999....

1 = 0.9999....

-------

The other proof involves doing long division slightly "wrong" (but still mathematically sound).

1= 1 / 1

1 / 1 in long division (using | for long division sign due to a lack of something better):

1|1.0000000

instead of saying 1 goes into 1, 1 time, say it goes in 0 times. Instead of saying it goes into 10, ten times say it goes in 9 times. repeat forever.

0.999
1|1.0000
9
10
9
10
9

------

basically, the reason we get repeating decimals is because our number system is not perfect - it lacks the ability to provide a simple way to express these numbers.

If we use a different number system (such as binary like computers or base 20 like the ancient Mayans) we end up with different fractions repeating.

For example, in the base 3 number system, 0.33333.... is written simply as 0.1 (the first digit after the dot represents thirds).
On the other hand, 1/2 expressed in base 3 is a repeating number!

yes:
1/9= 0.111111111...
2/9=0.222222222...
3/9=0.333333333...
4/9=0.444444444...
5/9=0.555555555...
6/9=0.666666666...
7/9=0.777777777...
8/9=0.888888888...
9/9=0.999999999... or 1

yes

This question has already been asked.
http://answers.yahoo.com/question/index;_ylt=AuOls78boZL7CGhoxyTZi_Dty6IX;_ylv=3?qid=20080320035617AAQcacN&show=7#profile-info-5LqRrWYKaa