# Does .99 repeating equal 1?

• ### I don't really care.

• Total voters
0

#### Spawn of God

##### Diabloii.Net Member
Does .99 repeating equal 1?

hey all. even tho school is over im still thinking about math. thats just crazy.
anyway i cant decide wat is true: does or does not .99 repeating equal 1? ive heard many different arguements for each side, and i want to know the truth. vote and explain urself please.

#### AeroJonesy

##### Diabloii.Net Member
Yes. Now there can be no more debate.

Why does this question always come up in the forum? It's not open for debate, because there's nothing to debate.

yes.

10 char

#### 5Ws

##### Banned
Yes and that's final.
*shoots himself for having to see yet another .99=1 thread*

#### Freemason

##### Banned
Unless you can come up with an infinately small number that can go between .99 repeating and 1, then yes it's the same.

#### Spawn of God

##### Diabloii.Net Member
actually if u think about it .00 repeating with a 1 on the end could be that inbetween number. also if one number can equal a different number, then the entire mathmatics system would fall apart. just as 4 does not equal 7, then .99 repeating must not equal 1.

#### mhl12

##### Diabloii.Net Member
5Ws said:
Yes and that's final.
*shoots himself for having to see yet another .99=1 thread*
what about 1.9999 repeating? Does that equal 2? :lol:

edit: there was a mathatical way of proving .9999 repeating equals 1 (involving fractions). I forgot how it went. Anyone wanna help out?

#### piff

##### Diabloii.Net Member
I gotta go with Spawn of God. One digit of pi being off means that pi isn't pi, just as one digit short of 1 isn't one.

#### Freemason

##### Banned
Spawn of God said:
actually if u think about it .00 repeating with a 1 on the end could be that inbetween number.
No little Johnny, 2 + 2 not using quantum mechanics does not equal five.

#### dirkdig

##### Diabloii.Net Member
.999...x10=9.999...
9.999...-1(.999...)=9
9/9=1
therefore, .999...=1

Too bad it's not mathematically accurate.
.999... is the LIMIT of x as x approaches 1. It's infinitely close to 1, but not 1.
Sorry.

#### AeroJonesy

##### Diabloii.Net Member
Spawn of God said:
actually if u think about it .00 repeating with a 1 on the end could be that inbetween number. also if one number can equal a different number, then the entire mathmatics system would fall apart. just as 4 does not equal 7, then .99 repeating must not equal 1.
How can a number repeat forever, but have an end? Answer me that, and maybe I'll consider your point.

#### Spawn of God

##### Diabloii.Net Member
dirkdig said:
.999...x10=9.999...
9.999...-1(.999...)=9
9/9=1
therefore, .999...=1

Too bad it's not mathematically accurate.
.999... is the LIMIT of x as x approaches 1. It's infinitely close to 1, but not 1.
Sorry.
yea ive seen lots of equations like that...urs isnt to good i think it actually goes something like this.

X=.9 repeating
(multiply both sides by ten)
10X=9.9 repeating
(subtract X from both sides)
9X=9
(divide both sides by 9)
X=1

of course, there is alot of rounding in step 2 and 3 of this equation, not to mention the entire thing is done assuming that .99 repeating equals 1 (which isnt true)

#### Spawn of God

##### Diabloii.Net Member
AeroJonesy said:
How can a number repeat forever, but have an end? Answer me that, and maybe I'll consider your point.
ahh, but if a number can repeat forever and not have an end, then there will always be a small fraction of value at the end of .99 repeating, therefore it could never be 1

#### Jigga-Scrooge

##### Diabloii.Net Member
.99... = .99...
1 = 1
.99... does not = 1

thats my stand on it, and im not changing it.

##### Diabloii.Net Member
Spawn of God said:
ahh, but if a number can repeat forever and not have an end, then there will always be a small fraction of value at the end of .99 repeating, therefore it could never be 1
Why are we having this argument again?

OK ... lets go this way:

1-.999... = 0.000000 ...

Anything but a zero is wrong

QED

#### jmorocks

##### Diabloii.Net Member
Spawn of God said:
yea ive seen lots of equations like that...urs isnt to good i think it actually goes something like this.

X=.9 repeating
(multiply both sides by ten)
10X=9.9 repeating
(subtract X from both sides)
9X=9
(divide both sides by 9)
X=1

of course, there is alot of rounding in step 2 and 3 of this equation, not to mention the entire thing is done assuming that .99 repeating equals 1 (which isnt true)
Assuming that "0.99999...." did have an end, then the last digit is being rounded.

Let X=0.9 repeating, made up of infinite number of digits, which I will call Y.

If X was written out, then it would have Y digits.
Multiplying X by 10 increases the number of digits by 1, or Y+1, because you have to add a 0 at the end.

Y-(Y+1) does not equal 0, therefore the last digit is being rounded and 9X cannot equal 9.

So 0.9 repeating is just approaching the limit of 1, but is not equal to 1. It's just an irrational number that cannot be fully written out, just like Pi. Sure you can calculate Pi to millions of digits, but there is no end. Same with Euler's number e.

Ever heard of a Mobius strip? Take a strip of paper, twist it halfway and tape the ends together. It only has 1 side that repeats but never ends :lol:

##### Diabloii.Net Member
.99 reapeting get infinetly closer to 1 but is not 1 because .09 is 10 time smaller than .9 using this information that goes on infinetly it get smaller and smaller untill it is not comprehensible by most human minds (not mine) just like the thoery that space goes on forever this is not comprehensible by ANY human mind because space supposedly goes on faster than we can think just like .9999999 goes on faster than we think infinetly geting closer to 1 in smaller and smaller amounts

#### AeroJonesy

##### Diabloii.Net Member
Spawn of God said:
ahh, but if a number can repeat forever and not have an end, then there will always be a small fraction of value at the end of .99 repeating, therefore it could never be 1
You can't talk about the end of the .999 repeating. It doesn't exist. This is a fundamental math concept.

I think we all agree that 1/3 = .33333 repeating. Multiply both sides by 3. I think you'll be pleasantly surprised.

exactly

10 chars

#### Freemason

##### Banned
jmorocks said:
Ever heard of a Mobius strip? Take a strip of paper, twist it halfway and tape the ends together. It only has 1 side that repeats but never ends :lol:
What about the sides of the paper? You hatemonger you, biased against the sides of paper!