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I'm not really sure if this thing belongs in this category,but I'll ask, Why 3.333333333... x3 =10,but not 9.9999999999...? Or,does 9.999999999... equal 10?It doesn't sound correct to me very much,so can anyone give me an explanation? Thank you all for reading and please do give me a reply if you know the answer to my question.


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The Genius wrote:I'm not really sure if this thing belongs in this category,but I'll ask, Why 3.333333333... x3 =10,but not 9.9999999999...? Or,does 9.999999999... equal 10?It doesn't sound correct to me very much,so can anyone give me an explanation? Thank you all for reading and please do give me a reply if you know the answer to my question. Just a quick stab at this! 3.3 is a repeater, so we get 3.33333r>>>>>> 3.333333333...X3 = 9.999999999r.... It will never make a full 10 and it is usually expressed as 9.99r,or to as many decimal places as required, the 'r' being repeater.
To use something that it is impossible to stop calculating, try Pi which is 3.14159, but for normal calculations it is used as 3.1416.
Pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679 8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273 724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609....................>>>>>>
http://en.wikipedia.org/wiki/Pi While I live I grow.


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I think you just mean rounding off, to a certain number of significant figures. But that does not make sense because you must have met that already, so I am not sure what you are asking?
just in case
3.33333333.....recurring
when you round it, to for instance 4 significant figures, the fifth is 3, which is below 5 so the last digit is not rounded up 3.333 to one significant figure, similarly 3
but, when you have 9.999999999....recurring whenever you try try to rounnd it, it will round up to the next value of 10. but you cannot write 9.99910 under the decimal number system. It discards the final zero as meaningless and interprets it as 9.9991 which is entirely the wrong value.
You can only add significant final values of 0 on the left hand side of the decimal point 1, 10, 100 etc. these have value, they do not mean the same as 1
so 9.9999. round that with next digit  9. So this rounds up the previous digit by 1, which makes 10, so the extra value feeds all the way back, until you meet a number where you can add another number without rounding up. This is on the upper value end of the number  you can add a single digit to a new 'tens' column and make 10.00 which to 2 significant figures rounds up to (edit, to one sf also, which is the problem: see below) 10
the disadvantage is that when you have a zero here, you cannot tell whether it means zero or is rounded from something else eg to 2 significant figures 10.000 10.111 and 9.999 all round up to 10
that is why you use the notation 1 x 10^1 so you can put the zeros on the right hand side of the decimal point to show they are significant eg to 4 significant figures 9.999 x 10^0 1.111 x 10^1 1.000 x 10^1 would round up to, in order 1.00 x 10^1 1.11 x 10^1 1.00 x 10^1 etc since the .999 is recurring, it will never come to the point where it does not round up to 10. The 'missing' 0.0000000...recurring...001 is so small, it cannot be shown under this number system. the decimal number system is incredibly powerful, but is is not perfect for all uses. That is why you use pi in equations and do not insert the values until you absolutely have to. It is why you keep manipulations such as divisions and square roots as expressions, without working out a numerical value, until you absolutely have to. Decimal notation is a precision tool for many applications, but for other it has it drawbacks, like any tool. So, good question. I think the answer is that you are using the 'wrong' tool to express it!
edit but the only normal situation where you have 3.333r (recurring), is where you have tried to express 10/3 in decimal notation, which results in a recurring decimal, which can only ever be written as an approximation. Multiplying by 3 produces another recurring decimal but does not remove the approximation. Keeping it in fraction form would give 10/3 x 3 = 10. With no approximations.
edit, don't know if Ray's link said all that anyway. As you can probably see, I work these things out during the post as I go along!


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Now, I ain't no Einstein, or nothing....and I started learning math in the first half of the last century, so I may be a bit rusty. However, the way I learned it is 3X3=9.0 and 3.3X3=9.9 and 3.333X3=9.999. No matter how many more 3's you put there, it will NEVER equal 10. On the other hand, if you divide 10 by 3, you get 3.33333r as you write it and the 3's to the right of the decimal will go on and on and on.....without ever becoming a 4. Even by the rules of rounding off, you still only get 3.333 to however many decimals you wish to take it. I hope that it is still true that 3X3=9. If not, then better go back to school and learn some more ciphering.
"When you don't know where you are going, you have to stick together just in case someone gets there."  Ken Kesey


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Actually, 3.333... * 3 = 10 = 9.999...
The reason is simple,
1/3 = .333... correct?
and 1/3 * 3 = 1
Thus 1/3 * 3 = .333... * 3 = 1
And therefore 10/3 * 3 = 3.333... * 3 = 10.
I find this strange also, but due to the axioms that math is based on, this necessarily must be the case. The one I am thinking of says that for any number, there is precisely one other number that operates as it's inverse. By inverse I mean that if you have 4, then 1/4 is it's inverse since 4*(1/4) = 1. And so 3 must have only one inverse also, which can be represented in various ways, the two we've discussed being 1/3 and .333...
It's also very important to hold in your mind that .333... =/= .333
.333 can be represented as a fraction, .333 = 333/1000 Just as .333... can be 1/3, but they are not the same number.
I think the whole thing is most confusing because due to constraints on the human mind we have trouble really understanding a number that repeats forever.


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I see no problem in accepting that 9.999.... is equal to 10, only the equality must be taken in the sense of limit, that is if taking sufficiently many 9's, we can get arbitrarily close to 10 (I don't want to be too formal, in mathematics this is expressed more precisely).
Put in a little different way:
lim 9.99...9 (exactly n 9's) = 10 as n approaches infinity.


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science is an attempt to approximate truth and maths is an attempt to approximate reality.... (that means I am being facetious!)


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Why does 0.999... = 1?But remember that mathematics is invented by humans.
*


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The Genius wrote:I'm not really sure if this thing belongs in this category,but I'll ask, Why 3.333333333... x3 =10,but not 9.9999999999...? Or,does 9.999999999... equal 10?It doesn't sound correct to me very much,so can anyone give me an explanation? The simple explanation is that 3.33… is an approximation in decimal notation of (10 ÷ 3), that is 10 ÷ 3 = 3.33… Because division is defined as the inverse operation of multiplication, this implies that 3 X (10 ÷ 3) = 3 X 3.33… and 10 = 3 X 3.33…
"Make it go away, Mrs Whatsit," he whispered. "Make it go away. It's evil."


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This is one example showing that decimal representations are not unique, viz., that 1 and 0.999... represent the same real number. Formally, this is easy to see by, e.g., setting x = 0.999... and subtracting this from 10 x = 9.999... and then solving the resulting equation 9 x = 9 for x.
One has to keep in mind that a decimal representation of a (nonnegative) real number x is actually a limit of a series, i.e., it is defined as x = n_0.n_1 n_2 n_3 ... = limit_(N>Infinity) Sum_j n_j / 10^j, where the sum is taken from j = 0 to j = N, and 10^j stands for 10 power j, and where the allowed integer numbers n_j range between 0 and 9 if j > 0.
The analogous considerations hold, of course, also for 9.999... and 10, and 99.999... and 100, etc.


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Jean_extraterre wrote:One has to keep in mind that a decimal representation of a (nonnegative) real number x is actually a limit of a series, i.e., it is defined as x = n_0.n_1 n_2 n_3 ... = limit_(N>Infinity) Sum_j n_j / 10^j, where the sum is taken from j = 0 to j = N, and 10^j stands for 10 power j, and where the allowed integer numbers n_j range between 0 and 9 if j > 0.
Ah, so the calculus rears its ugly head.
"When you don't know where you are going, you have to stick together just in case someone gets there."  Ken Kesey


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A broad discussion and generalizations of this issue can be found here: http://en.wikipedia.org/wiki/0.999...


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Here are a couple more links on the subject: This oneWhich also has a link to this one. "Shut up, she explained."  Ring Lardner


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Thank you all for giving me replies(thar,thanks for coming back so many times though I was not online.I am busy being a student)However I'm not really very clear yet since you have different opinions.
What I wanted to know is that why 3*3=9,but 3.33333...*3 isn't 9.99999...? thar,according to you,the number has been approximated,but (Please don't laugh for the next sentence),I've tried the calculator in google,where I typed 10/3.Of course,it was 3.3333(It doesn't show r or ...).I multiplied it with 3,and the answer was 10. You might think I'm a moron since what I said was 10/3*3=10,and you might probably think,"of course!".Yes,I know this,this is so simple. However I want to know why 3*3=9,3.3*3=9.9,3.33*3=9.99,3.333*3=9.999,and so on,then,respectively,3.33333...*3=9.99999...(I don't write 'r' since it may be confused with the radii of a circle).But it's 10.Why?
Any real genius?(I'm not really one,I think you got it)Please help though this is not anything urgent.That's nothing related to what Im learning in school now...
Thank you anyway.
By the way,Ray,did you recite pi by yourself or did you 'copy and paste' it?I admire you if you memorized it.(I've recited 300 decimal places and my friends say I'm sick...)
Once again


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TG, 3.333r is, for all calculations (excluding those that need infinitesimal accuracy) normally expressed as a fraction, eg: 3+1/3rd. If we also use this regarding 9.999r where we will get 9+9/10ths which is rounded up to 10.
Pi, in fractions is commonly shown as 22/7 (3+1/7th) and is sufficiently close enough to enable us to use it almost every calculation we would encounter in normal usage. I have used it to calculate in surveying and it has never produced a measurable error.Re: By the way,Ray,did you recite pi by yourself or did you 'copy and paste' it? I admire you if you memorized it.(I've recited 300 decimal places and my friends say I'm sick...)TG, if you can memorize Pi to 300 decimal places you have an excellent memory and there is no reason for your friends to say that you are 'sick'. If you are not displaying this knowledge in a boastful way, then they are jealous and trying to drag you down to their level when they should be striving to reach your level.(simply psychology!) One of my sons(now 38 years old) was a 4 unit maths student, also dux of his school. His friends(sic) constantly called him 'professor'. This upset him severely, which, would have had a detrimental affect on his application to his study if it was not for the support of his tutors and family.
Now, did I type Pi to all those decimal places? I am not far short of my 72 birthday, my brain cells are dying at a faster rate than my body can replace them.
What is copy and paste? I have 'Clag' and 'super glue', can you use them in any way? While I live I grow.


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the thing about pi is that you start off having to use the value... and the further you progress in maths or physics, the more complex the expressions, the more likely it is to cancel itself out. You end up leaving it there, except for brief excursions into giving an answer as a numerical value, because chances are another one will come along and cancel it! I did know it to about 3 dp (for rounding off to 2dp) but I let my calculator do all the hard work. After all, it is a peaceful, perfect pi, and putting any effort into remembering the digits seems to go against its restful spirit


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thar wrote:the thing about pi is that you start off having to use the value... and the further you progress in maths or physics, the more complex the expressions, the more likely it is to cancel itself out. You end up leaving it there, except for brief excursions into giving an answer as a numerical value, because chances are another one will come along and cancel it! I did know it to about 3 dp (for rounding off to 2dp) but I let my calculator do all the hard work. After all, it is a peaceful, perfect pi, and putting any effort into remembering the digits seems to go against its restful spirit It's true, pi does not like having its mysteries revealed. 4 decimal places has always been plenty for me. I read somewhere about how the state of Indiana nearly voted to make pi equal to 3.2. Fortunately, they did not approve the measure! "Shut up, she explained."  Ring Lardner


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early_apex wrote:thar wrote:the thing about pi is that you start off having to use the value... and the further you progress in maths or physics, the more complex the expressions, the more likely it is to cancel itself out. You end up leaving it there, except for brief excursions into giving an answer as a numerical value, because chances are another one will come along and cancel it! I did know it to about 3 dp (for rounding off to 2dp) but I let my calculator do all the hard work. After all, it is a peaceful, perfect pi, and putting any effort into remembering the digits seems to go against its restful spirit It's true, pi does not like having its mysteries revealed. 4 decimal places has always been plenty for me. I read somewhere about how the state of Indiana nearly voted to make pi equal to 3.2. Fortunately, they did not approve the measure! I am not flying in Hoosier planes!
*


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Numbers were assigned before as nomenclature before any ordered organized system of names that makes and sense in a deeper, bigger picture, higher order sort of way.
And even if we understood any of the discovered languages we use to speak or write our thoughts so that others who cannot understand how to recognize how to communicate using lesser known sensory perception, until a person is practiced at knowing, everything we speak, write, hear, or observe no matter how much we try to be precise, is only employing communication that is used for convenience.
I say "discovered" because I as understand or choose to to believe, Human Being discovered spoken and written languages in the same sense that we discovered certain principles and patterns that hold true (aka formulas) which are expressions that put into words the result of specific behaviors.
We didn't invent 2=2+2=31=42=two, and we aren't prophets because we recognize that jumping off a six story building with a concrete landing will result in high probability of death the same as we aren't prophets because we recognize that jumping off a twelve story building with nothing obstructing the fall through the surface area layer ocean of air that divides the oceans of water and ocean of air, with a concrete landing will result in Death for a living Human Being which means the legal resident spirit will be immediately evicted. I used the term "legal" to communicate with words the sense that the resident spirit very much so belonged or deserved that house that it resided in and could easily forfeit it's residency at any point in time before the natural dynamic lease expires, when it leaves regardless of the will, testament, and desires it has the freedom to carry out. I included the term "legal" because the overwhelming majority of "people" do not comprehend the way things exist in realms were hearers and knowers do not mistake "I" for "E" OR do not recognize full communication of shared thoughts instead of nomenclature for convenience like calling me Dusty on the street, as opposed using a more full version of any my language name in any realm (first, middle, last, etc...,etc...,etc...) OR my numbered name (any random number in infinite places to BOTH the right and left of the arc as humans know it, as well as any sphere of existence of outer infinite expansion to larger numbers or inner infinite filling in of smaller spaces that anything exists on any curve)
because Human beings have a hard time understanding the difference between laws that are obeyed without the need for enforcement, where forces do not have to waste time observing because the hear and KNOW with much more accuracy then most human remember because nearly none of them know how to communicate in more definite ways that are less convenient, left without any doubt or need to second guess and while their are no misunderstands, there is an awful lot of unnecessary trouble created by refusal to comprehend the meaning of honesty EVEN THOUGH the existence of human beings are allowed entrance into these realms one lifetime at a time so long as they choose to practice life AS IF they understood and recognizes the subtle spelling difference but unmistakable difference in meaning between the words egal and legal and yet they are afforded every convenience of the highest order of consciousness, even though they are given immortal awareness but confuse it with a physical permanence yet because they only choose to accept/understand the convenience of these priceless gifts, they are without a doubt too foolish or stupid to realize it is that choice to not see beyond convenience that will imprison their existence to a realm where forces can be free to exist without the obligation of enforcement because existences are respect as opposed to taken for granted.
Much like humans take for granted that every numbers they will ever know by any name, even it it is a very casual one time use to count how many other chances they will be gifted a physical life in an order as high as Heaven, and whether or not they understand the only name they do actually know in it's infinite entirety (without using a close enough to be true in their infinitely convenient unthankful disrespectful life) is zero, nothing
they just don't get that any other name is less the full name, of it's true name, even when it reaches it's limit and begin back filling into fullness of life, and then and only then it is not respectful to assume estimations to be the limit of truth, AND EVEN THEN you wouldn't catch me slapping or spitting or otherwise attempting cheat an unmarked agent of truth and deliferer (deliverer) of Justice to those who are unjustly treated by the too stupid continue life yet were mistakenly granted a third and sometimes even more FULL chances to choose to accept gifts that can be eternally renewed, that thought those forces are not carried out by me in any way shape or form, they are very much present and are very much impatient and will not continue to listen to me and my insistence that everyone here Is capable of understanding, if only the right words are spoken or written, even though it obviously is NOT true, but the only careless assumption I know is worth stating to those forces, because I know there is at least one more who will change their mind and decide to choose life as a Human Being in Heaven...
To be concerned of the fate of the world is not bad, but bearing false witness is to not be


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Dusty,
After giving considerable thoughtful attention to the items previously mentioned, it is, therefore, obviously of consequence that indeterminate to a measured metaphoric sort of anomalous cognizance framed ideally by the heretofore unsubstantiated claims, all pertinent to the view in question, it must be, having at once been recognized as a nonsequitir, both officially and by the periphery of attendant lay persons, as adjunct to the governing dynamic of general authority at large, deemed erroneous in both content & context to the relevant, relative position of the derivative values therein. Notwithstanding, nor in isolation from the central theme, to wit: a more cogent summation of the necessarily complex organizational boundaries, as with respect to precedence, terms of disclosure, specifically briefed, as cognates with the "purpose superior" function of streamlining these proceedings as time weighs upon the assemblage, all numeric considerations and actualities aside, of increasingly agitated disenfranchised humanity.
And I hope this makes my point, in reference to your post, perfectly clear.
Cheers, Ab...aka...kirk
"Now" is the eternal present.


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Ahoy cap`n kirtland,
Yes, cherrios, wheaties, and wrike krispies. In short, what I am saying with written word, is this Earth, was always then, is now, and will forever be Heaven. If somewhere deep down or anywhere, a person thinks they may wish to experience life living as a Human Being in a fully recognized Heaven, it would be a good idea for said person to realize the golden rule, which more or less implies a follower first understands the concept of honesty.
That said, I bear my testimony that the wise way to behave at this point in point in time should you wish to live another life as a human being in Heaven, is to stand up for truth and honesty, speak out against all who do have an unmistakable inability to comprehend the concept of honesty and therefore do not correctly identify the distinct difference between right and wrong, truth and lies.
Which is another way of saying speak out against Republicans, speak out against our Govt., speak out against the firm stance taken by the governing body of the Mormon church, the Roman Catholic church, especially the CIA and any organization the creepeth into Nations, States, or County governments until they realize the great disservice they do to GOD and all Countries due to their fundamentally flawed understanding of Truth and therefore GOD.
As anyone who knows THE TRUTH, knows that before there was The Word, there was NOTHING BUT THE TRUTH
SO HELP ME GOD
and He will, He will help anyone who is not so blind they fear the hands and works or evil men, more than they care to be in alignment with Destroying Angels of clear light, who will not evil men, by any nomenclature such as foolish, stupid, blind, deaf or just plain dumb or otherwise ignorant remain in power when to do so would destroy the earth, Whose Name is Heaven.
Because Kennedy's Spirit will call Human Being Home again, but those responsible for his murder, no matter how much they truly believed they were doing the protecting the Free World, will not ever again call a human house home, not without forgiveness by the courageous Man they ignorantly slaughtered or they callous description Saul Pet gave to the resting place of one of that Great Man's temporal houses
To be concerned of the fate of the world is not bad, but bearing false witness is to not be


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Sorry about that Kirk,
Seems I let past experience have too much influence and let my viewpoint, which I did not clearly state is discounted as outrageous conspiracy theory, get me worked up after I realized a person or two had been having "a little fun with me" online only I didn't find it very humorous.
What I was saying among many other things, is that numbers, are just the first language we discovered, giving something a symbol to represent that which is already in existence no matter what we call it is not something man created. And it's the same story with nonnumerical words as they thoughts and objects they symbolize (aka the meaning) were not created by name and neither were the sounds and words that are the symbols that we call words, they were discovered. However nonnumerical language is nowhere near as "figured out" as the language of math, and right now I am too pissed off to calmly explain it, but I will soon,
To be concerned of the fate of the world is not bad, but bearing false witness is to not be


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Greetings My Earthbound, Incognito Friend Dusty,
Thanks for addressing my concerns in your last post, and try to not allow evil & ignorance to anger you. Evil will be what it is and do what it does. It cannot operate outside it's very nature. This is another truth. Truth preexists existence, that is true. We have merely discovered and employ these truths as we interact with the natural created order. I am referring to the advent of language that followed human discovery of the actuality of the numeric order of all that is, and can be known.
Peace to you Bro, kirk
"Now" is the eternal present.


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You cannot get back to ten from 3.333 it will not work. That fraction will always be missing. it got lost in the division. Anyone who says that 3.33333 times 3 equals 10 is mistaken. If that were so, then why doesnt the calculator show 10 when you myultiply? No, math is not as perfect and everyone brags it out to be.


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simomed wrote:You cannot get back to ten from 3.333 it will not work. That fraction will always be missing. it got lost in the division. Anyone who says that 3.33333 times 3 equals 10 is mistaken. If that were so, then why doesnt the calculator show 10 when you myultiply? No, math is not as perfect and everyone brags it out to be. I think you missed a detail. 3.333 ≠ 3.333 …The ellipsis mark after the decimal portion indicates a repeating pattern which will always be greater than the same expression without the repeats. As shown above, the real value can be computed with the ∑ sum. Thus 3 * 3.333 = 9.999, but 3 * 3.333 … = 9.999… = 10.
"Make it go away, Mrs Whatsit," he whispered. "Make it go away. It's evil."


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simomed wrote:You cannot get back to ten from 3.333 it will not work. That fraction will always be missing. it got lost in the division. Anyone who says that 3.33333 times 3 equals 10 is mistaken. If that were so, then why doesnt the calculator show 10 when you myultiply? No, math is not as perfect and everyone brags it out to be. The maths is fine. The equation 10= 3x 3.3333... is fine. The calculator is fine within its limits too. However, you could not accurately work out a calculation such as 3.12878599458637 x 9.1994787366477563 for example. Can you see why?
All good ideas arrive by chance Max Ernst


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I'll be back at 2.44948974278^2 PM, approximately.
In the beginning there was nothing, which exploded.


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One way to think about it is to realize that 9.999... is a rational number and therefore able to be represented by the ratio of two integers.
Let the symbols p and q both represent integers with q not being zero. Hence, I can write
p/q = 9.9999... and (1/10)(p/q) = 0.999999....
Subtract the latter from the former to get
(9/10)(p/q) = 9
Solving for (p/q) I get
(p/q) = (90/9) = 10.
Compare this to my starting point of (p/q) = 9.999999.... Hence, I must conclude that 9.9999...= 10
There are no limits here. It is exact. 9.9999... is just another way of saying 10.
You can try same reasoning and math trick on the number 45.4545..... to find it equal to the ratio of what two integers?


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I like pigs. Dogs look up to us. Cats look down on us. Pigs treat us as equals.


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Math is just imperfect sometimes. That's what me and math have in common.


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yasmin1 wrote:I like pigs. Dogs look up to us. Cats look down on us. Pigs treat us as equals. They also make really good bacon sandwiches. Only if you calculate the right amount of HP sauce to use though! LOL docendo discimus


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Weirdo101 wrote:Math is just imperfect sometimes. That's what me and math have in common. Maths was never my subject. I'm OK if I can use my toes as well as my fingers to count things on. docendo discimus


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