View Full Version : Can some math genius help me out?

ki4jgt

January 3rd, 2011, 12:42 AM

OK, something just occurred to me. If I have 3 equal parts of something which are all part of one whole, according the 100% standard we have, If I were to separate them, they should grow exponentially. If I use 1/3 1/3 is .3333333. . . So how does one divide by 3s when it comes to percentages and math?

markbabc

January 3rd, 2011, 12:44 AM

OK, something just occurred to me. If I have 3 equal parts of something which are all part of one whole, according the 100% standard we have, If I were to separate them, they should grow exponentially. If I use 1/3 1/3 is .3333333. . . So how does one divide by 3s when it comes to percentages and math?

Your wrong. basically you have a 3rd of a 3rd of a 3rd....... its like the 1/2 paradox. if i walk hald the distance between you and me forever i will never actually reach you because you can keep dividing by 1/2's

ki4jgt

January 3rd, 2011, 12:46 AM

round up.

But then if these three lines were part on one whole line:

---

Mathematically, one would have to be bigger than the others or the sum of all three would have to be bigger than the whole. Yet, that is not happening.

markbabc

January 3rd, 2011, 12:48 AM

But then if these three lines were part on one whole line:

---

Mathematically, one would have to be bigger than the others or the sum of all three would have to be bigger than the whole. Yet, that is not happening.

You just cant divide something equally into 3 pieces.

ki4jgt

January 3rd, 2011, 12:50 AM

Your wrong. basically you have a 3rd of a 3rd of a 3rd....... its like the 1/2 paradox. if i walk hald the distance between you and me forever i will never actually reach you because you can keep dividing by 1/2's

Quoting you this time, so it doesn't change. I can split 100 in half. 50 / 50 ok, but I can't split it into thirds.

lisati

January 3rd, 2011, 12:52 AM

Percentages (and arithmetic in general) are abstractions. Sometimes difficulties arise in achieving precision when relating the abstractions to the reality. I suspect that the OP's question relates to the limitations of the representation of an abstraction.

ki4jgt

January 3rd, 2011, 12:52 AM

You just cant divide something equally into 3 pieces.

I just devided something into 3 equal pieces.

1) - 2) - 3) - <all the same length>

markbabc

January 3rd, 2011, 12:53 AM

Quoting you this time, so it doesn't change. I can split 100 in half. 50 / 50 ok, but I can't split it into thirds.

i misunderstood your question so i edited it but my first post of round up applies.

100/3 = 33.3333333333going on forever

its an irrational number because it never ends. thus can never become a whole 100% because you cant add an irrational number to anything to equal a whole.

ki4jgt

January 3rd, 2011, 12:54 AM

Percentages (and arithmetic in general) are abstractions. Sometimes difficulties arise in achieving precision when relating the abstractions to the reality.

So is there a way to make up for that in Mathmatics?

Kalimol

January 3rd, 2011, 01:04 AM

Make up for it how? You can either use a lot of decimal points or stick to fractions. I mean, you've heard about the game of calculating pi, right?

Three isn't special, though. If you started with 99, that's divisible by three but not by two. The fact that .333333 looks like it has a three in it doesn't make it an integer. = )

lisati

January 3rd, 2011, 01:11 AM

So is there a way to make up for that in Mathmatics?

/me remembers something I learned in high-school about representing 1/3 as 0.3, but with a dot over the 3 to indicate that it repeats. I didn't do much study beyond school, and that was a long time ago.....so my head is beginning to hurt. :(

ki4jgt

January 3rd, 2011, 01:20 AM

/me remembers something I learned in high-school about representing 1/3 as 0.3, but with a dot over the 3 to indicate that it repeats. I didn't do much study beyond school, and that was a long time ago.....so my head is beginning to hurt. :(

Yeah, but it really doesn't describe it, b/c if it repeats then it's ever expanding. If it just stops, it doesn't acuratly represent it and if it is rounded up the parts become bigger than the whole.

I was thinking something like 3 (x + y) could = the entire 100% now if I could just figure x and y.

***Edit: Wow, just reread that duh moment here. but the general idea is, a way to equally represent 33.333. . . using equaled equation.

msandoy

January 3rd, 2011, 01:38 AM

Is this not why we have the "float" in programming. It is not an integer, and it will never be completely accurate, only degrees of accurate.

earthpigg

January 3rd, 2011, 01:57 AM

If I use 1/3 1/3 is .3333333. . . So how does one divide by 3s when it comes to percentages and math?

fractions are often more precise than decimals, as they are simply an exact ratio of one thing to another without any regard as to how many of them there are. the ratio 1/3 is exactly equal to the ratio 2/6, for example.

same with pi. 3.14156blablabla will never be precise.

but the symbol for pi is exact. it defines the ratio between a circle's circumference and its diameter, and can also be regarded as just another ratio... not particularly different than 1/3.

for whatever reason, many of our human brains find decimals easier to grok than fractions even though ratios/fractions are far superior.

in general, we should endeavor to be comfy with fractions. why bother with the inaccurate .3333[...] when we can do all the same mathematical operations with 1/3? we can divide, multiply, add, subtract, work with unknown variables, etc, without losing any accuracy.

Kalimol

January 3rd, 2011, 02:01 AM

Oh, I'd strongly disagree with that. A fraction is inherently abstract in a way that a decimal isn't, and both people and computers have to put a lot more work into handling them. I mean, human beings have limits. Never mind that measurements are often imprecise, which means that (literally) infinite precision isn't required. And there are rational numbers, too.

Yeah, but it really doesn't describe it, b/c if it repeats then it's ever expanding. If it just stops, it doesn't acuratly represent it and if it is rounded up the parts become bigger than the whole.

Like markbabc said, you're misunderstanding this a bit. It's not ever-expanding in the sense that you mean, but it does continue infinitely.

Look at it this way: As markbabc was saying, each time you introduce another digit, it's 1/10 as meaningful as the one before it, because that's how math works. = ) The difference between .3 and one third is in the one-hundredths column. (That is, that's the first digit to be 0 instead of 3.) The difference between .3333 and one third is in the one-hundred-thousandths column. You're thinking that because the digits go on to infinity, they should be significant, but they're not, because they also get smaller infinitely. In that sense, you can imagine the "last" digit, an infinite number of places out and thus .3 divided by ten to the power of infinity, to equal exactly zero.

3Miro

January 3rd, 2011, 02:10 AM

In decimal system, you can represent 1/2 and 1/5 accurately, however, you cannot easily represent 1/3. Same in percentages (which are decimal based). If you go to a ternary system, then 1/3 will be exactly 0.1. If you use "percentages" based on 60 instead of 100, you can use 1/3 as 20 "percent", we do that with time.

A computer is a binary machine, so it cannot represent 1/3 exactly (unless you use symbolic computations and/or lisp, but this is beyond the scope of this post).

In our "everyday" decimal system, you can represent 1/3 as either 1/3 or .33 with a dash (the dash goes on top, but I cannot write it on a forum editor). .33 with a dash means constant repetition of the number 3. Thus 1/3 + 1/3 + 1/3 = 1 and .33-dash + .33-dash + .33-dash = 1 (.33 dash is exactly equal to 1/3, the same way .99-dash is exactly equal to 1).

In the case of percentages, it is common for people to round. When they tell you 30 percent, they mean 30 parts of 100, but if you hear 33 percent, they often mean 1/3. However, the exact way this is computed may vary (i.e. depending on the software that the Bank or whatever institution is using and 1/3 cannot be represented exactly as a float or double).

ki4jgt

January 3rd, 2011, 02:18 AM

How is it not ever expanding like I said. If I have .3, .33 is larger than .3 and .333. is larger than .33 but .33 is not 1/3. and .3333333333333333333333333333333333333333333333333 3333 is not 1/3 so it would infinitely have to get larger to encompass itself.

NovaAesa

January 3rd, 2011, 02:48 AM

How is it not ever expanding like I said. If I have .3, .33 is larger than .3 and .333. is larger than .33 but .33 is not 1/3. and .3333333333333333333333333333333333333333333333333 3333 is not 1/3 so it would infinitely have to get larger to encompass itself.

The decimal representation of the number 1/3 will be infinitely large unless you use one of the more compact notations alluded to earlier in the thread (dots/dashes above repeating digits). So yes, it is "ever expanding" if you don't use these notations.

In other words, 1/3 is equal to the limit of the sum of 3x10^(-n) from 1 to n as n approaches infinity.

Kalimol

January 3rd, 2011, 03:02 AM

I think you misunderstood him. He's not just saying that it's an infinitely long number (it is, of course.)He's thinking that it would actually be infinitely large as a value, because it's an infinite number of digits. (Most of which are, of course, almost infinitely small.)

ki4jgt, .33 and .333 and point .3333 and so on are all larger than .3, but they're all also smaller than .34. You're adding a bit each time you expand a digit, sure, but that bit you're adding gets smaller each time. It doesn't matter that you're adding an infinite number of quantities to something when they're approaching infinitely small.

Here, you could approach it going the other way, too, like this: 1/3 is 1 - .66..., right? So as you get more precise from .6 to .66 to .666 to .6666 and so on, 1 - .66... keeps getting smaller. But it'll still never be less than a third.

ki4jgt

January 3rd, 2011, 03:10 AM

I think you misunderstood him. He's not just saying that it's an infinitely long number (it is, of course.)He's thinking that it would actually be infinitely large as a value, because it's an infinite number of digits. (Most of which are, of course, almost infinitely small.)

ki4jgt, .33 and .333 and point .3333 and so on are all larger than .3, but they're all also smaller than .34. You're adding a bit each time you expand a digit, sure, but that bit you're adding gets smaller each time. It doesn't matter that you're adding an infinite number of quantities to something when they're approaching infinitely small.

Here, you could approach it going the other way, too, like this: 1/3 is 1 - .66..., right? So as you get more precise from .6 to .66 to .666 to .6666 and so on, 1 - .66... keeps getting smaller. But it'll still never be less than a third.

I understand that, but mathmatically, it is getting larger each time. Which is an inacurate portrayal of 1/3. b/c unlike the 1/2 riddle the 1/3 can actually fit into our number system and gets infinitely larger indefinitately. So even though it can never go over 3.4 it will still continue to get larger, based on our math system and not a riddle.

AlphaLexman

January 3rd, 2011, 03:14 AM

So .3333333333... times 3 equals .9999999999...

But one-third times three equals one!

See: http://en.wikipedia.org/wiki/0.999...

koleoptero

January 3rd, 2011, 03:37 AM

This thread is so confusing I'm beginning to forget what I already know :lolflag:

The fact that you see 0.333333333... as an inaccurate representation of 1/3 doesn't mean that it is. The problem lies with the limits of the decimal numbering system. If you use a ternary (is that the correct word? I forget) representation system with 0, 1 and 2 as the symbols then 1/3 becomes 0.1 (if I'm not mistaken) which is just very nice looking.

Also you keep saying that "0.333333 keeps getting bigger the more 3s you put there". It doesn't, your representation of 1/3 becomes more accurate but the number 1/3 doesn't change.

Also another thing to say is that you can divide things by 3 and get accurate results. Any number of which 3 is a divisor for one. And there are ways to cut any length in thirds (pure geometrical ways without actually measuring something).

And last I want to point out that 1=0.999999... which most people can't get in their heads because it just seems irrational. Well any numbering system has that shortcoming. In binary 1=0.11111... and in hexadecimal 1=0.ffffff... If you want me to write a proof about it I will but if you use google it'll be better because I'll have to use oo and pdfs to make sense of it and it's 4am here atm.

-Phi-

January 3rd, 2011, 04:28 AM

The proof that 0.9(repeated) = 1 isn't that hard if you start with the assumption that for numbers to be different there must be a value between them. For example, 1 is a different value than 2 because 1.5 fits in between. Or 1.5 and 1.6 are different because 1.55 is in between. There is no value between 0.9(repeated) and 1 (try it in your head :)). So they're the same value. It's like 0.9(repeated) and 1 are so squashed together that nothing fits in between, so they must be the same.

0.3(repeated)*3 = 0.9(repeated) = 1

QED, I hope :)

ki4jgt

January 3rd, 2011, 06:04 AM

The proof that 0.9(repeated) = 1 isn't that hard if you start with the assumption that for numbers to be different there must be a value between them. For example, 1 is a different value than 2 because 1.5 fits in between. Or 1.5 and 1.6 are different because 1.55 is in between. There is no value between 0.9(repeated) and 1 (try it in your head :)). So they're the same value. It's like 0.9(repeated) and 1 are so squashed together that nothing fits in between, so they must be the same.

0.3(repeated)*3 = 0.9(repeated) = 1

QED, I hope :)

I just saying in theory, --- is three parts of one whole. Which is 33.33333- percent. I get that. Logically that is the only thing which can make sense. I just don't get how that and the fact that .3333 increases in size doesn't mathmatically force the object to logically expand in size also. Because if we measure something and it's .25 inches and something else is .255 inches, .255 inches is longer.

***EDIT: Not unless it's like potential and kenetic energy, only there when the other isn't, but then It wouldn't be 1/3 Ahhhhhhh! My brain hurts :-(

koleoptero

January 3rd, 2011, 06:31 AM

I just saying in theory, --- is three parts of one whole. Which is 33.33333- percent. I get that. Logically that is the only thing which can make sense. I just don't get how that and the fact that .3333 increases in size doesn't mathmatically force the object to logically expand in size also. Because if we measure something and it's .25 inches and something else is .255 inches, .255 inches is longer.

***EDIT: Not unless it's like potential and kenetic energy, only there when the other isn't, but then It wouldn't be 1/3 Ahhhhhhh! My brain hurts :-(

It doesn't increase. What you say makes no sense. 33.333333333... is the 1/3 of 100, it doesn't stop at some point. If you do then you have a different number than 100/3. There's no point at which it gets bigger. It's an illusion to think it'd grow above it.

I just remembered another weird illusion which says that, if you move with say 30km/h and I move with 60km/h and we have some distance between us, say 1km, then I'll never reach you, cause when I travel that 1km you'll have traveled another 0.5km, and when I travel that 0.5km you'll have traveled another 0.25km, and when I travel that you'll have travelled another 0.125km and so on. Even though the distance decreases with every step it'll take infinite steps to reach zero so I'll never reach you. Weird huh?

ki4jgt

January 3rd, 2011, 06:42 AM

It doesn't increase. What you say makes no sense. 33.333333333... is the 1/3 of 100, it doesn't stop at some point. If you do then you have a different number than 100/3. There's no point at which it gets bigger. It's an illusion to think it'd grow above it.

I just remembered another weird illusion which says that, if you move with say 30km/h and I move with 60km/h and we have some distance between us, say 1km, then I'll never reach you, cause when I travel that 1km you'll have traveled another 0.5km, and when I travel that 0.5km you'll have traveled another 0.25km, and when I travel that you'll have travelled another 0.125km and so on. Even though the distance decreases with every step it'll take infinite steps to reach zero so I'll never reach you. Weird huh?

Even though I get what you are saying, as I stated above. There is a difference in your punch line and what I am saying. In your punch line the finish line is at 2 miles. It is definate. Definable. In mine, there is no definition. The finish line itself is moving if we rely on the mathmatics of the situation. In real life, the only way to define it, is 33.3333- b/c that is the only thing which can define 1/3 but at the same time, It keeps the finish line moving at all times.

koenn

January 3rd, 2011, 07:14 AM

your problem is that you're trying to make sense of things by converting it to a 10-based fraction, while it's exactly that conversion that throws you of.

1/3 is 1/3 and that's all there is to it. trying to represent it as 3/10 (=0.3) or 33/100 (=0.33) or 333333/1000000 or whatever is what makes it inaccurate

As for mathematics and being accurate : mathematics represents 1/3 as 1/3 because that representation is accurate. You can blame math fort the fact that your brain prefers to see something like 333333/1000000.

Sam Fallow

January 3rd, 2011, 07:46 AM

Love this kind of thread, I was thinking about Fermat last theorem the other day.

However...

I just remembered another weird illusion which says that, if you move with say 30km/h and I move with 60km/h and we have some distance between us, say 1km, then I'll never reach you, cause when I travel that 1km you'll have traveled another 0.5km, and when I travel that 0.5km you'll have traveled another 0.25km, and when I travel that you'll have travelled another 0.125km and so on. Even though the distance decreases with every step it'll take infinite steps to reach zero so I'll never reach you. Weird huh?

So a car travelling at 60kph can never crash into a car travelling at 30kph. Brilliant, I can avoid accidents by driving faster than everyone else. :)

koenn

January 3rd, 2011, 07:54 AM

So a car travelling at 60kph can never crash into a car travelling at 30kph. Brilliant, I can avoid accidents by driving faster than everyone else. :)

You'd need a Zeno Paradox to do that.

ki4jgt

January 3rd, 2011, 08:10 AM

your problem is that you're trying to make sense of things by converting it to a 10-based fraction, while it's exactly that conversion that throws you of.

1/3 is 1/3 and that's all there is to it. trying to represent it as 3/10 (=0.3) or 33/100 (=0.33) or 333333/1000000 or whatever is what makes it inaccurate

As for mathematics and being accurate : mathematics represents 1/3 as 1/3 because that representation is accurate. You can blame math fort the fact that your brain prefers to see something like 333333/1000000.

What is 1/3 if it is not 10 based number in math or as my brain sees it. 1/3 literally translates into 1 devided by 3. That's why in programming you use the / sign.

koenn

January 3rd, 2011, 08:48 AM

What is 1/3 if it is not 10 based number

you've answered it yourself:

1/3 literally translates into 1 devided by 3.

but you should stop there. What you implicitly are saying is "1/3 translates into 1 divided by 3, with the result given as a decimal number".

In a decimal representation, the result of that division would be 0.333...(with an infinite row of 3s) --

but you can just as well see 1/3 as a number in itself. In math these are called rational numbers (as in the "ratio" between 2 quantities).

You have no problem seeing 0.2 as a number, do you ? What if I'd write it as 1/5 ?

Why would 1/3 be different, other than that you can not easily convert it to a fraction with 10 or 100 as denominator ? (and you only want that because you used to counting and calculating in a 10-based system)

ki4jgt

January 3rd, 2011, 09:20 AM

you've answered it yourself:

but you should stop there. What you implicitly are saying is "1/3 translates into 1 divided by 3, with the result given as a decimal number".

In a decimal representation, the result of that division would be 0.333...(with an infinite row of 3s) --

but you can just as well see 1/3 as a number in itself. In math these are called rational numbers (as in the "ratio" between 2 quantities).

You have no problem seeing 0.2 as a number, do you ? What if I'd write it as 1/5 ?

Why would 1/3 be different, other than that you can not easily convert it to a fraction with 10 or 100 as denominator ? (and you only want that because you used to counting and calculating in a 10-based system)

Actually, I'm used to both, which is why I never had to study math in school. I never did my homework but I always got a passing grade on my tests. B/c I always thought of them as interchangeable. I would convert the fractions to decimals and decimals to fractions in the middle of my tests. Which is why I am linking them now. Because they mean the same to me. Literally, I can't tell a difference.

***EDIT: and literally, if they represent real numbers, there still is no difference. 4/5 hotdogs is still 80% of the pack. or .80

koenn

January 3rd, 2011, 10:47 AM

***EDIT: and literally, if they represent real numbers, there still is no difference. 4/5 hotdogs is still 80% of the pack. or .80

now do the same with 1/6 slize of pizza

ziekfiguur

January 3rd, 2011, 10:59 AM

your problem is that you're trying to make sense of things by converting it to a 10-based fraction, while it's exactly that conversion that throws you of.

Yes, lets use a 9-based system (by that i mean a numeric system with only the numbers 0-8 ), 1/3 = 0.3

Giant Speck

January 3rd, 2011, 12:13 PM

100/3 = 33.3333333333going on forever

its an irrational number because it never ends. thus can never become a whole 100% because you cant add an irrational number to anything to equal a whole.

An irrational number is a number which cannot be expressed as a/b, where a and b are both integers.

33.333333333... = 100/3

a = 100 = an integer

b = 3 = an integer

33.333333333... is not an irrational number, as it can be expressed as the fraction a/b (in this case 100/3 since a=100 and b=3).

NovaAesa

January 3rd, 2011, 12:14 PM

Yes, lets use a 9-based system (by that i mean a numeric system with only the numbers 0-8 ), 1/3 = 0.3

And with the shiny new base 9 system, let's try to represent 1/2 :P

3Miro

January 3rd, 2011, 02:04 PM

Fractions and decimals are interchangeable since they represent the same thing. As someone pointed out earlier, if you have a list of digits 0.12345, this translates to 1*10^(-1) + 2*10^(-2) + 3*10^(-3) + 4*10^(-4) + 5*10^(-5). This is simple when things are finite. However, In the case of infinitely many digits like the .333... (I cannot write the dash on top of it), the sum turns into a limit, which goes into the land of Calculus and Zeno's Paradox. This is perfectly fine Mathematical theory, it is just that you are probably not there yet.

.33... (with a dash on top) is exactly 1/3 and .999... (again the dash) is exactly 1. Furthermore, this is true bu definition (if you understand limits), no proof is necessary.

Don't confuse the way to represent something with the actual thing. You can call me either by my alias 3Miro or by my real name, while those are different, it is still me that you are talking about. In the same way, 1/3 and .333...(dash) gives you two labels to refer to: "dividing a whole into three and taking only one part of it".

eriktheblu

January 3rd, 2011, 04:01 PM

and with the shiny new base 9 system, let's try to represent 1/2 :p

4.5?

3Miro

January 3rd, 2011, 04:17 PM

4.5?

Nope:

4.5 (base nine) = 4 + 5/9 = 41/9

If we start with 1/2, lets take a look at .44 (base 9). This means:

4/9 + 4/81 = 40 / 81

This is a little short of 1/2. Lets try another 4

4/9 + 4/81 + 4/729 = 364 / 729

This is closer, but not quite there. We can keep going, but with any finite representation, we will be a bit short. Thus we need to write it as a limit, in other words in a base 9 system:

1/2 = .444... (put a dash on top)

eriktheblu

January 3rd, 2011, 06:08 PM

And this is why I'm not a mathematician.

markbabc

January 3rd, 2011, 06:16 PM

An irrational number is a number which cannot be expressed as a/b, where a and b are both integers.

33.333333333... = 100/3

a = 100 = an integer

b = 3 = an integer

33.333333333... is not an irrational number, as it can be expressed as the fraction a/b (in this case 100/3 since a=100 and b=3).

http://www2.scholastic.com/browse/article.jsp?id=3753146

kthxbai

koenn

January 3rd, 2011, 06:20 PM

http://www2.scholastic.com/browse/article.jsp?id=3753146

kthxbai

Irrational number: A number in which the decimal portion never ends and doesn’t repeat

http://www2.scholastic.com/browse/ar...jsp?id=3753146

3333333333333333333

markbabc

January 3rd, 2011, 06:25 PM

http://www2.scholastic.com/browse/ar...jsp?id=3753146

3333333333333333333

ooo i should have read the entire thing of that....

ki4jgt

January 3rd, 2011, 10:13 PM

I'm still going with potential and kinetic here. Potential percentages the extra three they are. Look within yourself and the answers find you will. :-)

Potentially the PERCENTAGE could have as many 333333s as it needs. kinetically, it needs an infinite amount, so the percentage is merely the same as it always was and always will be b/c the potential is feeding directly to the kinetic. The potential is the kinetic. Therefore this equation is perfectly elastic or perpetual.

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