# 1/3 cannot be expressed in decimal form?

1. Jul 9, 2008

### Holocene

Somome told me this. So, this is wrong:

$$\displaystyle{\frac{1}{3} = 0.\overline{3}}$$

?????

2. Jul 9, 2008

### Dragonfall

Sure it can. What you wrote is the decimal form of 1/3.

3. Jul 9, 2008

### Holocene

It seems so obvious that it can be. But someone claimed "it's not allowed in college algebra"...

4. Jul 9, 2008

### tony873004

I did that once on a homework assignment: wrote 0.3 with a bar over the 3 instead of writing 1/3. My teacher, who had a great sense of humor, pointed it out to the class, explaining that the bar prevented me from using an infinite amount of paper to express my answer.

5. Jul 9, 2008

### epkid08

Doesn't that go against the definition of a rational number?

6. Jul 9, 2008

### Defennder

This appears to be yet another question on 0.999...=1 in disguise.

7. Jul 9, 2008

### Holocene

pi isn't rational, but that doesn't stop us from using it in algebra???

8. Jul 9, 2008

### epkid08

I wasn't talking about using irrational numbers in algebra...

I was saying that a number that can be expressed as a simplified fraction, can also be expressed as a repeating decimal. That's one of the definitions of a rational number.

9. Jul 9, 2008

### Holocene

My mistake. I now read your original post as advocating that, yes, you can in fact represent 1/3 in decimal form.

10. Jul 10, 2008

### arildno

You cannot write 1/3 in a FINITE series of decimals.

That does not prohibit, you, however, from inventing a symbol to signify an INFINITE series of decimals, by which 1/3 might certainly be written down.

11. Jul 10, 2008

### HallsofIvy

Staff Emeritus
No, it doesn't. A rational number is one that can be represented as a fraction. It doesn't mean that it cannot also be represented in other forms also.

12. Jul 10, 2008

### Ignea_unda

Was the person who told you this trying to tell you that 1/3 could not be expressed in a finite decimal? That would turn out to be a true statement. Otherwise I agree with all the above posts.

13. Jul 10, 2008

### epkid08

I don't understand your post. You're saying I'm wrong, but you're also agreeing with me?

14. Jul 10, 2008

### arildno

HallsofIvy responded to this:

His comment is entirely explicable due to the complete paucity of content in that post!

By an oversight, he didn't identify this with you:

This is NOT what you said in your first post, it is impossible to deduce the contents of this post from the first one, so given HoI's oversight, how should he have understood what your first post meant?

15. Jul 10, 2008

### epkid08

My first comment was directed at your initial post, "1/3 cannot be expressed in decimal form." I responded, "[If 1/3 is not equal to .3~] Wouldn't that go against the definition of a rational number?" Which it does. How are people confused by this?

16. Jul 10, 2008

### uart

Don't worry epkid08. I realized that your first reply was a direct response to the original poster and took it the way that I'm sure you meant it to be interpreted.

Some people (quite understandably) thought that you were responding to the immediately previous reply and that made it look a little like you were saying the opposite of what I (and I'm sure others) understood you to be saying.

17. Jul 10, 2008

### yenchin

Might be a good idea to quote which ever post you want to reply to...

18. Jul 10, 2008

### epkid08

Who are you talking to? how ironic

19. Jul 10, 2008

### uman

This is off-topic, but I've always wondered why many people who refuse to believe that 1 = 0.9... readily believe that 1/3 = 0.3...

20. Jul 10, 2008

### sketchtrack

Reminds me of 1/2+1/4+1/8+1/16+1/32...=1