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# .9 Repeating Equals 1? Answered

HI! I am wondering if .999...=1? I mean if 1/3=.333 and 1/3+1/3+1/3=3/3 and 3/3=1. So wouldn't .333...+.333...+.333...=1? But it actually equals .999... not 1. I googled this question and I got many different answers
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For example...(someone wrote):
I'm not really into math, but a friend brought something up to me today that really seemed very strange. (For the duration of this post, .999 will mean .9 repeating unless otherwise specified- just for the sake of ease)
.999=x
10x=9.999
10x - x = 9x
9x=9
1x=1.
.999 = 1.
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Someone else wrote:
Numbers are fake. They are a manifestation of our minds to describe something, similar to words. Just because we say "red" doesn't mean something is red. what is red? Languages and math are very similar. Math is universal...at least for our planet though. .999~ does not = 1. But what .999~ repeating represents, does in fact equal what 1 represents.

No-one will ever be able to comprehend infinity, os its time to stop trying. Think of space and the universe. IT IS GROWING. how can it continue to grow with no stop? what is there to contain it? WE need something to contain it in order for us to understand it. We need a stopping point, but there is none.
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So who is correct? Do you agree that .999...=1? Or .999... does not equal 1?

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## Discussions

1/3 is an imperfect decimal. so 1/3 in decimal form is not 0.333 etc. because if it was and you took the infinite numbers and added them together you would get 0.9999999 etc. so 1/3 cannot be turned into a decimal form evenly.

0.999 repeating does not exist as a rational number. no fraction equals 0.999 repeating

Nope, always a decimal point less.  No slingle number expect for one can equal one.  1>.99999999999999999999999999999999 and always will be.  If it will go on infinitley, it i will still be less.

actually, I barely got a B in my maths test, but I am pretty sure that .999 does not equal one, it is just a tiny bit less correct? but then again, a tiny bit becomes an even tinier bit, and that will keep happening until it gets to 1, except it can't quite get to 1, because the size of something is infinite, big or small. this should be question of the month.

1-.999...=0.000...
.999... is infinitesimally smaller than 1 yet it remains smaller.

However, 1/9=.111...
so 9/9=1, yet .111...x9=.999...

it is a mathematically unanswerable question, as there are mathematical proofs supporting both answers.

The problem isn't unanswerable though with the question given you are right firefreak, 0.999 is a little smaller.  You just have to use a different kind of math.  By writing the problem like this(see pic) you get 0.9999... to an infinite number of nines.  This, when you reach infinity, equals one.  There are interesting uses to this type of problem but that is out of the scope of the post.  I like that you googled first BTW, shows actual interest.  As for the "No-one will ever be able to comprehend infinity" guy.  He is full of it.  We cannot perceive infinity but there are a lot of mathmaticians out there who effectively comprehend and use infinity to solve some pretty interesting questions.  Hope this helps.