100 questions linked to/from Is it true that $0.999999999\dots=1$?
27k views

### Is 1 divided by 3 equal to 0.333…? [duplicate]

I have been taught that $\frac{1}{3}$ is 0.333.... However, I believe that this is not true, as 1/3 cannot actually be represented in base ten; even if you had ...
576 views

### Is $0.9999…$ an integer? [duplicate]

Just out of curiosity, since $$\sum_{i>0}\frac{9\times10^{i-1}}{10^i}, \quad\text{ or }\quad 0.999\ldots=1,$$ Does that mean $0.999\ldots=1$, or in other words, that $0.999\ldots$ is an integer, ...
4k views

2k views

### How do I express 0.999(9) as a fraction? [duplicate]

I'm noob in math. If 0.333(3) is 1/3, 0.666(6) is 2/3, then 0.999(9) is what? If 3/3 and 0.999(9) is the same, then how can I express one of them without expressing the other?
607 views

### I'm puzzled with 0.99999 [duplicate]

Possible Duplicate: Does .99999… = 1? After reading all the kind answers for this previous question question of mine, I wonder... How do we get a fraction whose decimal expansion is the ...
1k views

### Is 4.99999… exactly equal to 5? [duplicate]

I'm a student of 10th std. Recently our teacher asked a Question that "Is 4.999...equal to 5 or not?" Everyone said that is isn't equal or it is approximately equal. Teacher too agreed to that. But ...
321 views

### 0.999… = 1? What is the secret? [duplicate]

If x = 0.999... (a) -> 10x=9.999... -> 10x-x=(9.999...)-(0.999...) -> 9x = 9 -> x = 9/9 = 1 (b) x = 0.999 (a) = 1 (b) ? So... what is the right explanation for this occur? I know that exists a ...
287 views

### Why does $0,\bar{9}$ equal $1$? [duplicate]

I am finding hard to understand why $0,99999..... = 1$ I have the following proof: Let $x$ be $0,9999...$ then $10x = 9,999...$ So $10x - x = 9,999 - 0,9999$ $9x = 9 \rightarrow x = 1$ From a ...
219 views

### If $0.999\cdots = 1$ Then Does $\frac{1}{10^\infty} = 0$? [duplicate]

Recently I stumbled across a, to me, rather strange idea. I was messing around with the proof of $0.999... = 1$, when I figured that what $0.999...$ means is that those are all nines. That way I came ...
### Fractional/rational form of $0.999…$ [duplicate]
Is it possible to express $0.999...$, a repeating number, as a fraction? Or as a ratio of two numbers? Basically all (my) attempts at the problem cancels all the terms and returns $1$. Is it even ...