## Is 0.9 recurring equal to 1?

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- CheeseLord
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### Is 0.9 recurring equal to 1?

What do you think?? This is a question I debated with my parents

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### Re: Is 0.9 recurring equal to 1?

That is a good question.

Also: Did JW leave his peanut butter in here?

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Also: Did JW leave his peanut butter in here?

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### Re: Is 0.9 recurring equal to 1?

No.

At least in my opinion. (Which isn't possible because this is a fact question)

Because, lets say we had .99999 right? so plus .00001 would make it 1. right? So needing that .00001 makes it so that repeating it does not equal 1. Plus, if the answer is yes, and it was recurring forever, it would go more than one.

I got a C in Geometry in the 2009-2010 school year, so quite possibly I'm wrong. Gambit might know, he teaches Math.

At least in my opinion. (Which isn't possible because this is a fact question)

Because, lets say we had .99999 right? so plus .00001 would make it 1. right? So needing that .00001 makes it so that repeating it does not equal 1. Plus, if the answer is yes, and it was recurring forever, it would go more than one.

I got a C in Geometry in the 2009-2010 school year, so quite possibly I'm wrong. Gambit might know, he teaches Math.

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- CheeseLord
**Posts:**147**Joined:**February 19th, 2009, 11:07 am**Location:**Knagla

### Re: Is 0.9 recurring equal to 1?

The thing is, this question pits two mathematically accurate facts against each other, so it depends on which one is true

1/3 +2/3 = 1 ...

but 0.9 recurring does not equal 1 ...

and HomerJ: Am I missing a joke here ??

1/3 +2/3 = 1 ...

but 0.9 recurring does not equal 1 ...

and HomerJ: Am I missing a joke here ??

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### Re: Is 0.9 recurring equal to 1?

The answer is yes, and it can be proven.

Take a=0.9999999...

Take b=1

10*a = 9.999999...

9*b = 9

9*b + a = 9.9999999...

Therefore: 10*a = 9*b + a

Implies: 9*a = 9*b

Implies: a = b

That is just one of the proofs, I believe there are more.

Take a=0.9999999...

Take b=1

10*a = 9.999999...

9*b = 9

9*b + a = 9.9999999...

Therefore: 10*a = 9*b + a

Implies: 9*a = 9*b

Implies: a = b

That is just one of the proofs, I believe there are more.

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- PeterPorty
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### Re: Is 0.9 recurring equal to 1?

0.9 recurring

damn, ninja'd, but yeah....

**is**in fact equal to 1. if you turn the decimal number to a fraction, you get 9/9, and 9/9=1/1 and 1/1=1. Therefore, yes, 9 recurring=1.damn, ninja'd, but yeah....

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- CheeseLord
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### Re: Is 0.9 recurring equal to 1?

Those mathematical proofs are very nice ones . BUT, I don't see how it detracts from the fact that

0.9999....... DOESN'T equal 1 Like Hulavuta, You have to add 0.00...01 somewhere along the line for it to become 1

Like 0.49 recurring is not equal to 0.5

At least, this is what most lower school maths teachers tell us.

0.9999....... DOESN'T equal 1 Like Hulavuta, You have to add 0.00...01 somewhere along the line for it to become 1

Like 0.49 recurring is not equal to 0.5

At least, this is what most lower school maths teachers tell us.

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- Pentarctagon
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### Re: Is 0.9 recurring equal to 1?

1/3 = 0.3 repeating. 1/3 * 3 = 1 while 0.3 repeating * 3 =0.9 repeating. therefore 0.9 repeating = 1. on the other hand, that 0.00.....01 shouldn't be able to magically materialize out of nowhere. its probably just one of those things where it is mathematically possible but logically not possible (at least that's how I see it).

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### Re: Is 0.9 recurring equal to 1?

PeterPorty: Fractions and Decimals both exist for a reason. 2/3 isn't exactly .6 repeating, because if 6 is two(2/3), then that means that 1 is 3, and 6+3 is 9, not 10.

So therefore .9 repeating might equal 9/9, but decimals can have tiny differences that fractions cover up. (Like the example above)

So therefore .9 repeating might equal 9/9, but decimals can have tiny differences that fractions cover up. (Like the example above)

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~Sierra

The Southern Chains, a fanfic

*“The difference between winners and champions is that champions are more consistent."*~Sierra

### Re: Is 0.9 recurring equal to 1?

Where you are making your mistake is that the nines go on infinitely. There is no end to them, so if you add 0.00...01, you will end up with 1.00...00999...Those mathematical proofs are very nice ones . BUT, I don't see how it detracts from the fact that

0.9999....... DOESN'T equal 1 Like Hulavuta, You have to add 0.00...01 somewhere along the line for it to become 1

Because of this, there is no number in existence that can be added to 0.999... that will result in 1 (other than 0)

Last edited by Joram on July 1st, 2010, 8:41 pm, edited 2 times in total.

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### Re: Is 0.9 recurring equal to 1?

I'm assuming he meant that it would stop at one point, just far in. Does your proof only work with the only infinite 9's or does it also work with the nines stopping somewhere?

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The Southern Chains, a fanfic

~Sierra

The Southern Chains, a fanfic

*“The difference between winners and champions is that champions are more consistent."*~Sierra

- CheeseLord
**Posts:**147**Joined:**February 19th, 2009, 11:07 am**Location:**Knagla

### Re: Is 0.9 recurring equal to 1?

but that doesn't mean that 0.999... is one, just like 0.49 recurring isn't 0.5Joram wrote: Because of this, there is no number in existence that can be added to 0.999... that will result in 1.

Hulavuta: I'm talking about infinite 9s BTW

Last edited by CheeseLord on July 1st, 2010, 8:41 pm, edited 1 time in total.

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- PeterPorty
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### Re: Is 0.9 recurring equal to 1?

Hula. Nope. read what Pent said. anyway, it is the same...

http://en.wikipedia.org/wiki/0.999...#Algebraic_proofs

http://en.wikipedia.org/wiki/0.999...#Algebraic_proofs

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### Re: Is 0.9 recurring equal to 1?

Yes 0.99999... equals 1. The confusion only comes from a misunderstanding of number's representation. If you take a ruler and agree that any decimal number between 0 and 1 can be placed somewhere between the 0 and 1 marks. And, similarly, agree that any point between those marks has a decimal representation (possibly infinite like 0.9999...). Then 0.9999.. should be there too, but where? If we assume that it's not on 1, then there is a little space between 0.999.. and 1, and points between them can be represented by numbers. But how do you write a number bigger than 0.9999.. and smaller than 1? It's impossible. Thus, our initial assumption (0.999.. is not on 1) was false, and they are, in fact equals.

You must accept that one number (that is any point on the ruler) may have different numeric representations. Your intuition mislead you because when there is not an infinite number of decimals, things seems simpler. But you already accepted that 0.000... equals 0, why not accept that 0.999... equals 1. If there is a rule like "infinite sequence of 0 can be rounded to the lower integer", why not have a rule like "infinite sequence of 9 can be rounded to the upper integer"?

You must accept that one number (that is any point on the ruler) may have different numeric representations. Your intuition mislead you because when there is not an infinite number of decimals, things seems simpler. But you already accepted that 0.000... equals 0, why not accept that 0.999... equals 1. If there is a rule like "infinite sequence of 0 can be rounded to the lower integer", why not have a rule like "infinite sequence of 9 can be rounded to the upper integer"?

### Re: Is 0.9 recurring equal to 1?

To put what Alink was saying a little differently (as in, saying the same thing with different word choice), suppose you have two

No matter how close you put them, there will always be some space in between (ignoring for the moment the physical theories that there is a "minimum distance"). You will be able to represent a point on that distance as a decimal or fraction. However, there are no points in between 0.999... and 1. Therefore, since there are no points between them, they must be the same number.

The reason I do this is because it is a very good point.

**different**positions on a ruler.No matter how close you put them, there will always be some space in between (ignoring for the moment the physical theories that there is a "minimum distance"). You will be able to represent a point on that distance as a decimal or fraction. However, there are no points in between 0.999... and 1. Therefore, since there are no points between them, they must be the same number.

The reason I do this is because it is a very good point.

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