# For you maths-people as I'm confused.

1. May 18, 2004

### Lorentz

How is it possible that I can write (for example) 1/3 and be 100% accurate while I couldn't write the same number in decimals being just as accurate?

It has to do with our choice of system. But what is it exactly? I don't seem to grasp it or isn't there anything to grasp?

2. May 18, 2004

### matt grime

it's nothing to do with a deficiency in the representative powers of the system, but with your intent to use a word such as "accurate" and hope it means something mathematically for it to translate as 'looks pretty' and 'doesn't take up too much space on the paper'.

3. May 18, 2004

### Lorentz

Thanks for clearing that up... though I still think it's weird.

4. May 19, 2004

### Simon666

There isn't anything to grasp, depending on the system you use, you will not be able to accurately display certain fractions, like for example 1/3 in both binary and decimal system you would need an infinite amount of numbers. That is an entire issue when doing math in the computer and one that has already frequently caused me problems. It is not weird, just plain annoying.

5. May 20, 2004

### TALewis

Can't you write it in decimals like this:

$$\frac{1}{3} = 0.\bar{3}$$

Aren't both ways 100% accurate?

6. May 20, 2004

### Integral

Staff Emeritus
Or you could write it

$$.1_3$$

That's base 3. The existence of the real number line is independent of the any representation of points on the line. In a Real Analysis course, where the properties of the Real Line are explored in depth, such representations are not used, thus the results apply to all representations.

Last edited: May 20, 2004
7. May 21, 2004

### Stevo

Actually, I don't think that's true. If you multiply your equation there through by 3, you'll see why.

8. May 21, 2004

### matt grime

please say you're not about to start another pointless 1 is not equal to 0.999... thread. they are equal, end of story

9. May 21, 2004

### TALewis

Yeah:

$$1=0.\bar{9}$$

I think that's an often asked question. But it's true. Or that's what they tell me.

10. May 21, 2004

### Zurtex

Before you go there, it is true and there are many many proofs that as stated above $1=0.\bar{9}$. If you are interested please try and learn them and see why they are right then just trying to argue them wrong illogically.

11. May 21, 2004

### Stevo

Ok, I apologise for making that comment. I found a proof, I'm convinced!

12. May 30, 2004

### Lorentz

Does this notation mean: 0.999999... (going on infinately) ?

13. May 30, 2004

### Gelsamel Epsilon

You can't get exactly 1/3 exept through drawing eg.

Triangle with two 1cm sided sides and a hypotonuse the Hypotonuse will be exactly = to Sqrt of 2

14. May 30, 2004

### TALewis

Yes, that's the so-called "bar" notation. The line indicates a repeating sequence of numbers. Here is another:

$$\frac{1}{11} = 0.\overline{09}$$

Here two digits 09 repeat continuously (0.09090909...).

15. May 30, 2004

### Integral

Staff Emeritus
As mentioned above, in every base, there are some points on the Real line which cannot be represented in a finite number of digits. A very interesting example of this is:
$$.1_{10} = .000 \overline {1100}_2$$

The implication of this is that any time .1 is used by a computer in a calculation it MUST be rounded off.

16. May 30, 2004

### robert Ihnot

Accurate Representation

Of course, you could write 1/3 as .3 with a bar over the three to represent an unending decimal, but this is again just a mater of "what looks pretty," and has nothing to do with the calculations in a computer. You see that 0, and 5 are divisable in base 10, and thus, 1/2 = .5. Now if you want to do math to the base 3, then we have 1/3=.1 (base 3) same as we have in base 10, 1/10 = .1 (base 10). By changing bases we solve such problems!?

17. May 30, 2004

### jcsd

For reference bar notation isn't the only way of writing recurring decimals:

$$0.\bar{3} = 0.\dot{3}$$

$$0.\overline{30} = 0.\dot{3}\dot{0}$$

$$0.\overline{307} = 0.\dot{3}0\dot{7}$$

I think it's preferable to use dots when writi git out by hand as it makes mistakes less likely.