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**junior****Member**- Registered: 2006-09-22
- Posts: 2

I always think that 1/3, is always an infinatley small number away from 0.333... because as you add more 3's it gets a bit closer but even if you ad an infinate number of 3s, which is what recurring numbers are, then its an infinatley small number away. Isn't saying 1/3 = 0.333... a bit cheating because you should say 0.333... ≈ 1/3?

Just so you know, I have heard of the 0.999... = 1 thing, but recurring numbers still make no sence to me...

*Last edited by junior (2006-09-22 08:55:42)*

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

We actually have quite some posts here on the forum, where we discuss this very matter. An example is http://www.mathsisfun.com/forum/viewtopic.php?id=658. To be honest, this is one of the hardest things for me to explain when I, for example, help friends. By that I mean explain it so they actually get some kind of understanding about recurring decimals, and not just accept it because they don't want to *waste* their time on the topic. (Hah! as if working with maths could actually be wasting time)

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,616

It is because we keep thinking that "recurring" is like "walking" or "running", we think it happens a step at a time. But it is actually fully formed, there is no "last digit", it is infinitely long already.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Infinity is very hard to conceptualize. That is because *infinity doesn't exist in our world*. Or at least as far as we know. Everything is always finite. Even time.

What you have to do is realize that inifinity, as of now, only exists in the math world. It does have very many useful applications to our real world, but it doesn't exist in it.

And on top of that, the math world is very hard because most people think it should follow common sense. But it doesn't, at least, not always.

That being said, try actually dividing 1 by 3. After the first step, you get:

__0

3) 1

Second:

__0.3

3) 1.0

0.9

----

.1

Third:

__0.33

3) 1.00

0.9

----

.10

.09

----

.01

And keep going. What are you going to be doing? Getting a 3 each and every time. An infinite amount of them, in fact.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**elite-mathlete****Member**- Registered: 2006-07-16
- Posts: 40

I had a bit of trouble with recurring numbers in 9th grade. It can definitely be confusing. I just learned to write them like this:

_

0.333

and just kept going with my math.

Maybe the helicopter, maybe it's made of chocolate.

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

Isn't one digit enough?

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**elite-mathlete****Member**- Registered: 2006-07-16
- Posts: 40

yeah but I just did it with three.

Maybe the helicopter, maybe it's made of chocolate.

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**cray****Member**- Registered: 2006-10-05
- Posts: 29

What you have to do is realize that inifinity, as of now, only exists in the math world. It does have very many useful applications to our real world, but it doesn't exist in it.

Isnt that a theory rather than a fact? Otherwise you are saying that there are limits to the extent of space and time, and no-one can know if that is true or not unless they have absolute proof.

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