are 1 and 0.999 reccuring are the same number?

Question

if you divide 1 and 0.999 reccuring then you get 0.333 recurring for both

Answer 1

Although clearly they are not the below does seem to show otherwise:

let s=0.9 recurring

therefore 10s=9.9 recurring

10s-s=9s=9

therefore s=1

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Answer 2

As you probably know (since you asked the question), they are indeed one and the same (pardon the pun). Several valid proofs have been shown. Every argument to the contrary relies on unsupported statements.

One answer claims that these proofs are "bogus", but how can one take that argument seriously when it invokes the claim that 0.999... recurring "is clearly not" a rational real number? It is the epitome of a rational real number in that it can be expressed as a repeating decimal!

In other words it is the ratio of two integers where the denominator is not zero (9 divided by 9). You can do the long division yourself, just keep carrying a remainder of 9 rather than zero (there is no limit involved in saying 9 goes into 90 nine times with a remainder of 9). This is just one more way to show it.

I vote with the guy that had the SAT score of 787.999... recurring!

Answer 3

if u divide 0.999 recuring by 3 then u get 0.333 recuring

If u divide 1 by three u get 1/3. the best way this can be expressed as a number is 0.333 recuring but this is not exactly true. However it is close enough not to matter unless you ask a question like this.

Answer 4

Yes - and you've explained it perfectly yourself.

It's really annoying how people who don't know what they're talking about try to answer these questions as if they do. For example, the moron below me has tried to prove this fact in his own little moronic way, and put wikipedia as his source.

If you actually click the link, you will see that the wikipedia article states "In mathematics, 0.999… is a recurring decimal which is exactly equal to 1. In other words, the symbols 0.999… and 1 represent the same real number."

It defeats the point of Yahoo answers if people try to be authoritative about something they're only bluffing with. Please, don't do it, if you have an opinion but not much evidence, say that you're not sure before you answer.

Answer 5

YES!

In the Real number system, given any two numbers you can always find infinitely many other Real numbers that fall between them. Very Cool fact about the Reals!

There are no numbers between 0.999... and 1, so they are the same.

Don't be fooled by the argument that you could just add another 9, because 0.999... already has all of them. That's what the recurring part means

Answer 6

calculaters only allow so many digits, so cuts the recurring numbers short. so is a rounded down version of the real thing.
i like this question, when 0.999 recurring for infinity would have to = 1 because to amount between the two is infinitely small, and how do you have something infinitely small?

Answer 7

This is an issue of precision. As a physicist, neither exactly 1, nor 0.9999... are measurable. I measure 1.00 plus or minus .01. Without specifying uncertainty, a number is useless anyway. I could tell you I drive 18.564897123 plus or minus 1 miles to get to work, and that is no different then had I said 18 plus or minus one, since the .5 digit was less than uncertainty anyway.

Now a mathematician will tell you that 1 and 0.9999... are two, different real numbers no matter how many nines you add. So it depends on what you mean. In the real world though, they are indistingushable.

Answer 8

The answer is yes. They are the same number.

Try performing a simple subtraction.

1 - 0.9 recurring

That would be 0.00000000000000000.........where do you put the 1 and the end. You can't because there is no end. So the answer is 0 and hence they are equal.

Not a real mathematical proof I grant you but it get to the heart of the matter

Answer 9

Wow, so many opinions. The two numbers (1 and .999 to infinity) are the same for mathematical and scientific purposes. Note that 1 minus .999 to infinity = 0.

Answer 10

Surely the infinite number of 3's would be different for both? Different infinities, no? Like the difference between the infinite set of odd numbers, and the infinite set of the 4 times table,( which has half as many numbers, but is still infinite).

Answer 11

They are equivalent. This is not an opinion, but fact. Anyone exposed to even slightly higher mathematics can verify this for you and will most likely know it as a trivial fact. A real number is defined by the least upper bound of a particular series. The least upper bound of 0.9+0.09+0.009+0.0009+... = 0.99999.... is 1