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# How close to 1 is 0.999...?

## Question

Or is .9999... equal to 1?

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is it .001?

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is it .001?

Nope. That would be a number greater than one.

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Or is .9999 equal to 1?

depends how you look at it:

view 1) .99999999 ? 1

duh!

view 2) look at it this way:

what is 1 - 0.9999999999999* ???

It would be:

0.0000000000000*1

But the 1 can never exist, there can never be an end, it is infinite

so 1 - 0.9999999999999* is equal to:

0.000000000000000000000000000000000000***************

1=1

i think so. Either that or a new level above infinity has to be created for the 1 to go

(like this: 0?1) or something

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it's

.0001

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Or is .9999 equal to 1?

Absolutely, 1=1 . Rounding off is a whole different method. It is as close as can be but, without rounding it off to 1, I still believe it is just a hair shy of 1.

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it's

.0001

.999... = 1

any number added to it will be over 1.

.999... is greater than .99999

If you add .0001 to .99999 you will have a number greater than 1, so obviously you will have a number greater than 1 if you add .0001 to .99999... That number will be 1.0001

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Absolutely, 1=1 . Rounding off is a whole different method. It is as close as can be but, without rounding it off to 1, I still believe it is just a hair shy of 1.

Nope. Not a hair shy. Check out the links.

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it's

.0001

Sorry, Thuhchris. The OP should have read "Or is .9999... equal to 1?".

I edited it just now.

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Sorry, Thuhchris. The OP should have read "Or is .9999... equal to 1?".

I edited it just now.

oh gottcha

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I read all the links. I just never needed to learn anything as such. That should be the first question given on a test for a potential CPA. It just may change many minds, and be interesting to see the answers.

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Yes I read about it a long back somewhere at the archimedes-lab pages.

There is no need to round off 0.9999... to get 1, it is exactly equal to one.

or in other words,

writing 0.9999.... is just another way of writing one.

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Here's an easy way to think about it.

1/9 = .11111...

9 * 1/9 = .9999999...

9/9 = 1

1 = .999999...

My math teacher taught us this.

Edited by Frost
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Yeah, that's one way. I think of it like this:

What is 1 - 0.99999...?

Look at these first:

1 - 0.9 = 0.1

1 - 0.99 = 0.01

1 - 0.999 = 0.001

1 - 0.9999 = 0.0001

etc

for an infinite number of 9's, the 0's go on forever. There is no difference with a bunch of 0's and then a 1

1 - 0.999999999... = 0

thus

1 = 1

Edited by unreality
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I love all this repeating number stuff!

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I didn't know you meant it was repeated forever.

becuase if it wasn't, then it would be possible.

EDIT: Typo

Edited by Thuhchris
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I got it...It's one decimal digit away from 1.

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another proof of it equalling 1 that I just thought of:

1/3 = .333333333etc

2/3 = .666666666etc

we know that 1/3 + 2/3 is 3/3, or 1

we also know that .33333etc + .66666etc = .999999etc

therefore .9999999etc must equal 1

Edited by unreality
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in a sense, you're right

but it's pretty much impossible for 1/3 to be put as a decimal or percent

but this is as close as you'll get

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1/3 = .3333333repeating

there's no "close"ness, they are exactly equal.

Since 1/3 * 3 = 1

.333333repeating * 3 = .999999repeating = 1

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.9 repeating to infinite is exactly equal to 1.

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but I just don't see it

the difference between .999... and 1, is infinitely minute

and 1 and 1 have no difference

there's a difference between infinitely minute, and no difference

so they aren't equal

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they are equal ;D

as this site puts it: Sorry, It Does lol

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