# Does 0.9999 = 1?

#### Goatworlds

##### New member
I'm trying to do my math homework today, and I need your help. Does 0.9999 equal 1? My friends say no, But i'm not exactly sure.

#### DrownedAmmet

##### Senior Member
It's a way for the decimal system to do thirds, the way they explain it is if you have 0.99999 with a truly infinite number of nines, then there is no number that can be higher than that without it being one, therefor it equals one

Kind of bullshit math wizardry, but you have to accept it if you want calculus to work easier

#### Pirate Of PC Master race

##### Rambles about half of the time
Baron Cimetiere said:
Goatworlds said:
I'm trying to do my math homework today, and I need your help. Does 0.9999 equal 1? My friends say no, But i'm not exactly sure.
Call me a lunatic, but I think you shouldn't ask for homework help on this site, but pick one that's more suited. The answer to your question in any case is that .99999 APPROXIMATES 1 through rounding, but cannot equal 1.

.999999... ~ 1
Yeah, what he said. Don't get help from here.

P.S:
1/3 = 0.33333.....
(1/3) * 3 = 0.999999... = 1

0.9999 does NOT equal to 1.

#### Revnak_v1legacy

##### Fixed by "Monday"
0.9 infinitely repeating is "equal" to 1 in most forms of mathematics, which likely includes the one you are doing your homework in.

#### mduncan50

##### New member
Revnak said:
0.9 infinitely repeating is "equal" to 1 in most forms of mathematics, which likely includes the one you are doing your homework in.
To be fair, he could be in grade 3 and learning rounding.

#### Fat Hippo

##### Prepare to be Gnomed
Legacy
Pirate Of PC Master race said:
Baron Cimetiere said:
Goatworlds said:
I'm trying to do my math homework today, and I need your help. Does 0.9999 equal 1? My friends say no, But i'm not exactly sure.
Call me a lunatic, but I think you shouldn't ask for homework help on this site, but pick one that's more suited. The answer to your question in any case is that .99999 APPROXIMATES 1 through rounding, but cannot equal 1.

.999999... ~ 1
Yeah, what he said. Don't get help from here.

P.S:
1/3 = 0.33333.....
(1/3) * 3 = 0.999999... = 1

0.9999 does NOT equal to 1.
"(1/3) * 3 = 0.999999" is incorrect because it assumes that 1/3 = 0.33333, which is not true. At most, 0.33333 approximates 1/3.

If you're multiplying fractions, don't turn them into decimals, because decimals will often be less precise than fractions. Another way of writing it would be 1/3 * 3 = 1/3 * 3/1 = 3/3 = 1, which is precise.

But really, we can't answer the OP's question without the context of what he's trying to solve.

#### Pirate Of PC Master race

##### Rambles about half of the time
Fat_Hippo said:
Pirate Of PC Master race said:
Baron Cimetiere said:
Goatworlds said:
I'm trying to do my math homework today, and I need your help. Does 0.9999 equal 1? My friends say no, But i'm not exactly sure.
Call me a lunatic, but I think you shouldn't ask for homework help on this site, but pick one that's more suited. The answer to your question in any case is that .99999 APPROXIMATES 1 through rounding, but cannot equal 1.

.999999... ~ 1
Yeah, what he said. Don't get help from here.

P.S:
1/3 = 0.33333.....
(1/3) * 3 = 0.999999... = 1

0.9999 does NOT equal to 1.
"(1/3) * 3 = 0.999999" is incorrect because it assumes that 1/3 = 0.33333, which is not true. At most, 0.33333 approximates 1/3.

If you're multiplying fractions, don't turn them into decimals, because decimals will often be less precise than fractions. Another way of writing it would be 1/3 * 3 = 1/3 * 3/1 = 3/3 = 1, which is precise.

But really, we can't answer the OP's question without the context of what he's trying to solve.
Which is why I out continuing dots(also known as Ellipsis), since I can't type in repeating decimals(https://en.wikipedia.org/wiki/Repeating_decimal).

Please read this wikipedia article on ellipsis, under "In mathematical notation" before continuing any further. (https://en.wikipedia.org/wiki/Ellipsis)

Or to put it simply,
An ellipsis is also often used in mathematics to mean "and so forth".
Please do not quote things I said out of context(particularly by excluding ellipsis from my quotes). I can type "I am ass" from your previous quote by splicing your quote(and deleting large amount of unnecessary characters), but you can't see me doing that.

#### Revnak_v1legacy

##### Fixed by "Monday"
mduncan50 said:
Revnak said:
0.9 infinitely repeating is "equal" to 1 in most forms of mathematics, which likely includes the one you are doing your homework in.
To be fair, he could be in grade 3 and learning rounding.
Then he would be under 12, and therefore ought to be banned.

#### BabySinclair

##### New member
1/3 is exactly one third of one. Numerically as a decimal, it is 0.33 repeating. There is no way to write the decimal notation because it does not perfectly divide. It is the precise third of the number 1. If multiplied by 3, it equals 1 because the precise third of a number multiplied by 3 equals the number. So 0.33 repeating * 3 equals 1 as 0.33 repeating is 1/3.

Now if the question is, "Does the finite decimal 0.9999 equal 1?" then the answer is "No." It is one ten thousandths away from being one. If the question is, "0.9999 repeating equal 1?" then the answer is "Yes" for the reasoning stated above. 0.9 (r) = 0.3 (r) * 3 = 1/3 * 3 = 3/3 = 1

It's an example of the Transitive property at work.

#### Fat Hippo

##### Prepare to be Gnomed
Legacy
Pirate Of PC Master race said:
Fat_Hippo said:
Pirate Of PC Master race said:
Baron Cimetiere said:
Goatworlds said:
I'm trying to do my math homework today, and I need your help. Does 0.9999 equal 1? My friends say no, But i'm not exactly sure.
Call me a lunatic, but I think you shouldn't ask for homework help on this site, but pick one that's more suited. The answer to your question in any case is that .99999 APPROXIMATES 1 through rounding, but cannot equal 1.

.999999... ~ 1
Yeah, what he said. Don't get help from here.

P.S:
1/3 = 0.33333.....
(1/3) * 3 = 0.999999... = 1

0.9999 does NOT equal to 1.
"(1/3) * 3 = 0.999999" is incorrect because it assumes that 1/3 = 0.33333, which is not true. At most, 0.33333 approximates 1/3.

If you're multiplying fractions, don't turn them into decimals, because decimals will often be less precise than fractions. Another way of writing it would be 1/3 * 3 = 1/3 * 3/1 = 3/3 = 1, which is precise.

But really, we can't answer the OP's question without the context of what he's trying to solve.
Which is why I out continuing dots(also known as Ellipsis), since I can't type in repeating decimals(https://en.wikipedia.org/wiki/Repeating_decimal).

Please read this wikipedia article on Elipsis, under "In mathematical notation" before continuing any further. (https://en.wikipedia.org/wiki/Ellipsis)

Or to put it simply,
An ellipsis is also often used in mathematics to mean "and so forth".
Please do not quote things I said out of context. I can type "I am ass" from your previous quote by splicing your quote(and deleting large amount of unnecessary characters), but you can't see me doing that.
I was not intending to offend, but I did not quote you out of context either, as the entirety of your post was contained in my quote, and the OP's post was obviously taken into consideration.

From a mathematical perspective, the statement "(1/3) * 3 = 0.999999..." remains untrue, independent of the ellipses, as 0.999999... will never precisely be equal to 1, but "1/3 * 3" will.

Again, I wasn't trying to anger you, but merely correcting you in a manner which I found relevant to the mathematical problem being discussed. (Since "1/3 = 0.33333..." is very similar to "1 = 0.9999....")

#### kurupt87

##### Fuhuhzucking hellcocks I'm good
Fat_Hippo said:
Pirate Of PC Master race said:
Fat_Hippo said:
Pirate Of PC Master race said:
Baron Cimetiere said:
Goatworlds said:
I'm trying to do my math homework today, and I need your help. Does 0.9999 equal 1? My friends say no, But i'm not exactly sure.
Call me a lunatic, but I think you shouldn't ask for homework help on this site, but pick one that's more suited. The answer to your question in any case is that .99999 APPROXIMATES 1 through rounding, but cannot equal 1.

.999999... ~ 1
Yeah, what he said. Don't get help from here.

P.S:
1/3 = 0.33333.....
(1/3) * 3 = 0.999999... = 1

0.9999 does NOT equal to 1.
"(1/3) * 3 = 0.999999" is incorrect because it assumes that 1/3 = 0.33333, which is not true. At most, 0.33333 approximates 1/3.

If you're multiplying fractions, don't turn them into decimals, because decimals will often be less precise than fractions. Another way of writing it would be 1/3 * 3 = 1/3 * 3/1 = 3/3 = 1, which is precise.

But really, we can't answer the OP's question without the context of what he's trying to solve.
Which is why I out continuing dots(also known as Ellipsis), since I can't type in repeating decimals(https://en.wikipedia.org/wiki/Repeating_decimal).

Please read this wikipedia article on Elipsis, under "In mathematical notation" before continuing any further. (https://en.wikipedia.org/wiki/Ellipsis)

Or to put it simply,
An ellipsis is also often used in mathematics to mean "and so forth".
Please do not quote things I said out of context. I can type "I am ass" from your previous quote by splicing your quote(and deleting large amount of unnecessary characters), but you can't see me doing that.
I was not intending to offend, but I did not quote you out of context either, as the entirety of your post was contained in my quote, and the OP's post was obviously taken into consideration.

From a mathematical perspective, the statement "(1/3) * 3 = 0.999999..." remains untrue, independent of the ellipses, as 0.999999... will never precisely be equal to 1, but "1/3 * 3" will.

Again, I wasn't trying to anger you, but merely correcting you in a manner which I found relevant to the mathematical problem being discussed. (Since "1/3 = 0.33333..." is very similar to "1 = 0.9999....")
That's only because derping was occuring and a decimal and fraction were being multiplied by one another, so you can choose to misinterpret.

But;
IF 1/3 = 0.3 recurring AND 3 * 1/3 = 1
THEN 0.3 recurring * 3 = 0.9 recurring = 1

#### Secondhand Revenant

Legacy
Yes, .999 repeating is 1. It can be proved multiple ways.

.9999...
.9 + .09 + .009 + ...
9 (1/10) + 9 (1/10)^2 + 9 (1/10)^3 + ...
Which is:
-9 + summation from n = 0 to infinity of 9 (1/10)^n

Using the formula a/(1-r) for geometric series where r < 1...

-9 + 9/(1-1/10)
-9 + 9/(9/10)
-9 + 10
1

People find it counterintuitive but it is equal to 1.

#### Pirate Of PC Master race

##### Rambles about half of the time
Fat_Hippo said:
Pirate Of PC Master race said:
Fat_Hippo said:
Pirate Of PC Master race said:
Baron Cimetiere said:
Goatworlds said:
I'm trying to do my math homework today, and I need your help. Does 0.9999 equal 1? My friends say no, But i'm not exactly sure.
Call me a lunatic, but I think you shouldn't ask for homework help on this site, but pick one that's more suited. The answer to your question in any case is that .99999 APPROXIMATES 1 through rounding, but cannot equal 1.

.999999... ~ 1
Yeah, what he said. Don't get help from here.

P.S:
1/3 = 0.33333.....
(1/3) * 3 = 0.999999... = 1

0.9999 does NOT equal to 1.
"(1/3) * 3 = 0.999999" is incorrect because it assumes that 1/3 = 0.33333, which is not true. At most, 0.33333 approximates 1/3.

If you're multiplying fractions, don't turn them into decimals, because decimals will often be less precise than fractions. Another way of writing it would be 1/3 * 3 = 1/3 * 3/1 = 3/3 = 1, which is precise.

But really, we can't answer the OP's question without the context of what he's trying to solve.
Which is why I out continuing dots(also known as Ellipsis), since I can't type in repeating decimals(https://en.wikipedia.org/wiki/Repeating_decimal).

Please read this wikipedia article on Elipsis, under "In mathematical notation" before continuing any further. (https://en.wikipedia.org/wiki/Ellipsis)

Or to put it simply,
An ellipsis is also often used in mathematics to mean "and so forth".
Please do not quote things I said out of context. I can type "I am ass" from your previous quote by splicing your quote(and deleting large amount of unnecessary characters), but you can't see me doing that.
I was not intending to offend, but I did not quote you out of context either, as the entirety of your post was contained in my quote, and the OP's post was obviously taken into consideration.

From a mathematical perspective, the statement "(1/3) * 3 = 0.999999..." remains untrue, independent of the ellipses, as 0.999999... will never precisely be equal to 1, but "1/3 * 3" will.

Again, I wasn't trying to anger you, but merely correcting you in a manner which I found relevant to the mathematical problem being discussed. (Since "1/3 = 0.33333..." is very similar to "1 = 0.9999....")
Oh. That's your problem. Good thing I have answer for that as well.

Please refer to wikipedia's article, "0.999..." under section "Algebraic proofs", "Analytic proofs", and "Proofs from the construction of the real numbers" before continuing the discussion.
(https://en.wikipedia.org/wiki/0.999...)

#### mduncan50

##### New member
Revnak said:
mduncan50 said:
Revnak said:
0.9 infinitely repeating is "equal" to 1 in most forms of mathematics, which likely includes the one you are doing your homework in.
To be fair, he could be in grade 3 and learning rounding.
Then he would be under 12, and therefore ought to be banned.
I wont tell on the kid if you don't.

#### veloper

##### New member
This is what wikipedia is for.

Over here you may hear any kind of answer. Hell even fucking Youtube is more suited. Look up to ViHart or Numberphile for the correct answer.

#### Secondhand Revenant

Legacy
Toast B.C. said:
The answer is simple even if people get too far up their own butts to admit it. (I have 3 friends exactly like this.)
No, 0.999999999 repeating does not equal 1. No tricks for multiplication of fractions and decimals will ever make them equal. Doing that 1/3= 0.333333333 line is about the same thing as running translations through google translate 8 times. It's fun, but the results aren't correct.
But it is damn near impossible to show the difference. Much like with 0, you can't show it, but treating them as something hey are not, creates false results.
They simply aren't, and it's something at just has to be accepted since people far smarter than all of us, who are paid to be as smart as they are, have to do calculations based on the difference. Saying, "close enough as makes no difference", will cause spaceships to explode. And if you have to make exceptions for differing levels of math, then you shouldn't be asking the question in the first place.
Again, these are just the arguments I have have seen in the past.
Yes, they are exactly equal. It's not even disputed by people who really know math. It's conclusive and just calling things 'tricks' doesn't actually show any error.

Translations have inaccuracies. 1/3 = .3 repeating is not inaccurate. Your comparison doesn't work.

And it doesn't even begin to address viewing it as an infinite geometric series which gives the same result

#### False Messiah

##### Afflicted with DDDS
Goatworlds said:
I'm trying to do my math homework today, and I need your help. Does 0.9999 equal 1? My friends say no, But i'm not exactly sure.
The most accepted 'proof' is:

x = 0.999...
10x = 9.999...
9x = 9.999... - 0.999... = 9
9x = 9
x = 1