The Metric System with Rounding is Garbage
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Voting Style:  Open  Point System:  7 Point  
Started:  10/6/2008  Category:  Science  
Updated:  9 years ago  Status:  Voting Period  
Viewed:  5,396 times  Debate No:  5660 
Debate Rounds (5)
Comments (26)
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If a system has to be corrected to produce accurate results then that system is flawed.
I submit the rounding function as the corrective function of the metric system. Therefore, the metric system with rounding is FLAWED. Operations involving rounding must be "fixed" by using a rounding function of some type. Multi step equations using the metric system are extremely succeptable to compound rounding errors. Proof: Sum(Product) * Markup% <> Sum(Product * Markup%) Research: Excel SpreadSheet Example of Compound Rounding Errors Across 100 Items Copy each formula and paste down the columns 100 times. Column A[1..100](ItemAmount) = ROUND(RANDBETWEEN(0, 10) + RAND(),2) Column B[1..100](CostPlusAmount) = ItemAmount*CostPlusPercent Column C[1..100](ItemTotalAmount) = ItemAmount + CostPlusAmount Column D[1..100](AdjustedItemAmount) = ROUND(ItemTotalAmount,2) Column E[1..100](RoundedAmount) = ItemTotalAmount  AdjustedItemAmount Column F[1](AccumulatedErrorAmount) = E[1] Column F[2..100](AccumulatedErrorAmount) = F[N1] + E[N] CHART(F[1..100) on the X axis of your graph a Change to a blank cell will result in an new set of 100 random items. The result that column E will contain an entirely new and RANDOM series. The accumulated margin of Error between the two functions Sum(ItemAmount) * Markup% and Sum(ItemAmount* Markup%) across different sets of items will vary randomly between 0.05 and +0.05 cents. Debate? Why should we use the metric system with it's inherent flaws? Because it lets simpletons count with their fingers? Because it's what all the COOL mathematicians use? Everything in nature is proportional, it would seem some other system, maybe a fractional system to be a much better solution than the metric system with it's rounding function and the chaotic nature imposed on every function that uses it. I for one loath rounding for anything other than SINGLE step equations such as approximations, averages, and statistics. It'll get you close. I would like to debate this with someone who understands the rounding functions such as truncate, and other floor/ceiling functions
I would like to thank my opponent for starting this debate and wish him the best of luck. In addition, I would ask that people only vote if they actually read the debate and vote based on who won this debate rather than what they already believe. With that said, let us begin. Rounding exist for these reasons: 1. Speed of computation 2. Ease of computation Although rounding makes numbers less precise, there are easier to use. For example, π is 3.14159265358979323846… Try to find the circumference of the circle and the result would not be pretty. Instead, in school, people would be more likely use 3.14 to represent π. What useful applications would you need a number for if it had more than a dozen digits after the decimal point. Truncation indicates "round toward zero" and although are rarely used in statistics and science, hey are still used in computer algorithms because they are slightly easier and faster to compute. Two specialized methods used in mathematics and computer science are the floor (always round down to the nearest integer) and ceiling (always round up to the nearest integer). People can't spend more than two minutes solving an equation that has to be exact when it contains a lot of digits behind the decimal point. Even the calculator won't help you be exact when working with irrational numbers. The metric system with rounding is NOT flawed because of the aforementioned reasons and it isn't garbage because speed and ease is important when using the metric system. The objective of rounding is often to get a number that is easier to use, at the cost of making it less precise. However, the accuracy will not be off more than a few integers. Vote for CON!!! Source: http://en.wikipedia.org... http://en.wikipedia.org... 

Thanks!
I appreciate your accepting the argument and overlooking my behaviour. I didn't realize this was formal. My apologies. First, I will address your first two points. Yes, I concur, the reason that rounding exists is for both the ease and speed of computation. BUT! at the expense of accuracy or error, which is what we are debating. I choose the position that this inaccuracy makes the metric system unsuitable for multi step equations with feedback. I concede your point that it works fine for single stage equations such as averages, conversions, statistics, etc. Again I attempt to iterate my position, The margin of error introduced by rounding increases with the time complexity of the problem and is exagerated through feedback and amplification. This accumulated error over time make the decimal/metric systems with rounding flawed. This flaw or amount of error is measurable. Case in Point: Look up the rounding issue on the targeting system for the Patriot Missle System. The compounded inaccuracies over extended periods of time rendered the Patriot Missle System targeting ineffective. There are thousands of algorithms where the accumulated error of rounding impacts the desired results. Simple equations do not suffer from compound rounding errors and therefore are not applicable to this debate. Do you want your aircraft landing systems subject to compound rounding errors? Some young coder writes you a Ground Level indicator and doesn't understand this, could put you off 10 feet from ground level. "For every action there is an equal and opposite reaction" even in mathematics. You cannot truncate or round up without consequenses. These consequenses are the core of my argument. Second, I will address your inclusion of irrational numbers as a proposition for your position. Irrational number are both number and function. Irrational numbers can only be modeled with the decimal/metric system. The rounding function combined with the irrational introduce complexity that cannot be easily modeled. Algorithms that include irrational number/functions introduce the problem of compound rounding at every step of the equation. The divergence between the right answer and the approximation become even more random and exagerated. Irrational numbers increase the accumulated error and further validate my position that the amount of error is large enough to consider the system flawed. Your apparent position that the decimal/metric system is neccesary for the ability to work with irrational and imaginary numbers will never be disputed by me. This debate is not on if we should or should not use the decimal/metric system, but the fact that the decimal/metric system IS subject to compound rounding errors AND the argument that this error indicates a flaw or not. Thanks! I appreciate your time. Don
I apologize for my inconvenience of time delay. I am being educated at high school, but I will continue our debate. I also apologize for vocabulary and inexperience. First, I agree with your statement that rounding exist if for both the ease and speed of computation but will inevitably create accuracy or error. However, the error of rounding can be decreased to the extent where rounding in the metric system is not flawed. Let me get you the definition of roundoff error: Roundoff error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value. Numerical analysis specifically tries to estimate this error when using approximation equations and/or algorithms, especially when using finite digits to represent infinite digits of real numbers. Increasing the number of digits allowed in a representation reduces the magnitude of possible round off errors, but any representation limited to finitely many digits will still cause some degree of round off error for uncountably many real numbers. Now all we have to do is to reduce the magnitude of possible round off errors: Although this kind of error is unavoidable for conventional representations of numbers, but can be reduced by the use of guard digits. In case you don't know what guard digits are, let me tell you: In numerical analysis, one or more guard digits can be used to reduce the amount of round off error. For example, suppose that the final result of a long, multistep calculation can be safely rounded off to N decimal places. That is to say, the round off error introduced by this final round off makes a negligible contribution to the overall uncertainty. However, it is quite likely that it is not safe to round off the intermediate steps in the calculation to the same number of digits. That is because round off errors can accumulate. If M decimal places are used in the intermediate calculation, we say there are MN guard digits. Even though round off errors can accumulate, guard digits can decrease the magnitude of it. Guard Digits are also used in floating point operations in most computer systems. Given 21 * 0.100 − 20 * 0.111 we have to line up the binary points. This means we must add an extra digit to the first operanda guard digitthis gives us 21 * 0.1000 − 21 * 0.0111 performing this operation gives us 21 * 0.0001 or 2 − 2 * 0.100. Without using a guard digit we have 21 * 0.100 − 21 * 0.011 this yields 21 * 0.001 or 2 − 1 * 0.100 This gives us a relative error of 1. Therefore we can see how important guard digits can be. Second, your case in point is the rounding issue on the targeting system for the Patriot Missiles System. I'm not familiar with the specifics of the programming related to those missile systems, but whenever I have to count with decimals I change my representation so I'm using integers. So instead of calling a millisecond 0.001s I call it just what it is, 1 millisecond. Then if I need to show something in seconds I just divide the milliseconds by ten for my output, but keep counting in milliseconds so that my data is not off. Computers have trouble with any number that is not an integer, and they would have just as much trouble with reciprocals of powers of two. Computers would not represent 1/32 as 1/32, but as 0.0009765, which is just another decimal number like 0.1. The downfall of the program wasn't the metric system, but a problem inherent with trying to accurately represent numbers that are not integers. The reason this bug occurred is because of a problem with storing time in a 24bit register. The problem is that time is stored to an accuracy of 1/10th of a second, but a 24bit register does not have enough precision to store 0.1, so a small fraction of each second is lost. The result is that the register used to keep track of time is off by 0.0001% of the amount of time that the system has been in operation. The problem is that computers do not store information as a standard decimal. Instead, they use binary code, which can not accurately store 1/10th of a second. But the REAL problem was not with inaccuracy, but with inconsistency. During one of the updates, Raytheon Labs, the developer of the patriot missile, had fixed the previously mentioned inaccuracy problem by creating code that used a pair of 24 bit registers to accurately make the time calculations. The problem was that that most, but not all of the time calculations made by the system were replaced by calls to the newer, more accurate function. So, the system was keeping track of the current time using a function that loses time in much the same way that a clock with a weak battery will gradually lose time. But, the system would track missiles, aim itself, and decide exactly when to launch it's own missiles using the internal clock, which was accurate. In effect, the system would use an accurate timepiece to decide where the missile is located and how fast it is moving, and when to fire the defensive missiles. But while waiting to fire the missiles, the system would use the less accurate clock to determine when it should fire. It was estimated that after running the system for twenty hours, the calculations made using the old algorithm and those made by the new algorithm differed by as much as 1/3 of a second[3]. A SCUD missile can travel more than one mile per second. Had the same piece of code been used for all time conversions, then the inaccuracy of the Patriot Missile would not have increased over time the way it did in this case. Instead, every time calculation would be off by approximately 0.000001 seconds, and the system would be much more likely to have defended against any missiles launched at it. This is a good argument for reuse of code whenever possible. Although the developers at Raytheon Labs had tried to replace all time conversions with calls to the new function, they missed a few and the result was a system that was less reliable than it would have been if they had chosen to ignore the conversion error. The above passage indicates that the problem was not actually rounding errors. At least one of these software modifications was the introduction of a subroutine for converting clocktime more accurately into floatingpoint. This calculation was needed in about half a dozen places in the program, but the call to the subroutine was not inserted at every point where it was needed. Hence, with a less accurate truncated time of one radar pulse being subtracted from a more accurate time of another radar pulse, the error no longer canceled. Fundamentally, the problem is that computers don't deal with numbers in any particularly sensible fashion. I think that you can build computers based on any numerical base, but i imagine they will be harder to create and manage (circuitwise). A better alternative is to build an emulator that performs base 10 arithmetic and runs on a binary computer, without making use of the available floating point operations to perform floating point operations (i.e. use the available logical operations exclusively). It would be slower, but cheaper. Therefore it is not the fault of the metric system that we have accumulated rounding errors but the computer's. The rounding errors can be minimized so we can say the the metric system with rounding is not garbage. Thank you for debating with me and correcting what I am debating for. I would like to thank my opponent for his meaningful debate subject and would like to request that this debate be judged solely on who was the better debate and for the factors listed in voting above. Sources: http://www.physicsforums.com... http://seeri.etsu.edu... http://en.wikipedia.org... http://en.wikipedia.org... 

First off, let me say you are brilliant!
I love your arguments. Your understanding of the problem is now clear. For the sake of position, I must pick at your arguments a little. On the following statement "However, the error of rounding can be decreased to the extent where rounding in the metric system is not flawed" The first part, that indeed the error of rounding can be decreased is true. However, your statement clearly indicates an understanding that this is indeed "error" and well, an error is a flaw isn't it? Your following explanation of rounding errors was ourstanding!!! You kick my butt on delivery. Your explanation of gaurd digits I found facinating. You have provided on of the more complex mechanisms for fixing rounding errors. You would make a fine programmer. But, your explanation itself includes the acknowledgment of the error I describe as well as provides a suitable mechanism for "fixing" it. If Work must be done to fix the result, is not the result wrong prior to the fix? Does it not follow then that the system is flawed? Remember, the argument is not about if we need it, but if it is indeed flawed. Your next point about the rounding error being in the computer is, I'm sorry to say, misinformed. The rounding error we debate is the result of mathematical rounding and all methods of rounding are subject to this. The rounding error in computers (OMG!!! you didn't go there) is further proof of the flaw we discuss. EVERY platform out there rounds different. Each has it's own "epsilon" or "very tiny" margin of error and they are different accross hardware platforms. Divide 1/3 then mulitply by 3 and your answers will NOT be the same. Even different CPU models yield different results. I can load a float on one platform with .09 and on the playstation it is .09. HOWEVER, if i load the same number on an x86 platform, i get .089999999999999999999999999 DO NOT count on floating point/decimal arithmatic doing what you think it will do on any CPU without a LOT of work. Your keyframe animations will be an abomination if you don't, I learned from experience Functions dependent on normal rounding, will have VASTLY different results on different processors. In Game Design, there are whole papers written on just how to write algorithms that work "cross platform" so the games you play look the same if you play on a playstation or xbox. The following article will explain the floating point specification much better than I ever could http://en.wikipedia.org... We don't have enough room here for cross platform rounding as it's a BIG problem. You said "But the REAL problem was not with inaccuracy, but with inconsistency" Both are problems, and there we are again...problem, error,.... flaw? Regardless of how small we make the error, it does not REMOVE the error. Is this, regardless of the scale or magnitude of the error, not a flaw? Flaw:  defect: an imperfection in an object or machine  "A crack or breach, a gap or fissure; a defect of continuity or cohesion; A defect, fault, or imperfection, especially one that is hidden" Every point you have made acknowledges the existence of the error. This error, no matter how small is still error. If you accept the definition of flaw as error, then you must concede that the decimal/metric system with rounding is indeed... Flawed and imperfect.
Thank you for complimenting me. I appreciate your comment. Due to inexperience, I didn't understand the problem at first, but I do now. Now I will question your points. Source: http://www.thefreedictionary.com... The definition stated by the Webster's New World Basic Dictionary of American English is: flaw (fl�) n. 1. a break, scratch, crack, etc. that spoils something; blemish 2. any fault or error Based from these definitions, I am forced to conclude that an error is indeed a flaw. HOWEVER, I have to question you about your knowledge about perfection. Do you know that nobody or nothing is perfect? Don't you know that everyone makes mistakes? Did you know that things can be improved? Based on knowing that you consider an error to be a flaw, I have to conclude that mostly everything is flawed, right? So all my schoolwork that doesn't have a 100 on it is flawed? So everything everyone does is flawed? The Wikipedia's definition of perfection is: Perfection is, broadly, a state of completeness and flawlessness. 3 different types of perfection can be listed as: 1. which is complete — which contains all the requisite parts; 2. which is so good that nothing of the kind could be better; 3. which has attained its purpose. Therefore you can see that nothing is perfect. The paradox of perfection ,although I don't know if you ever heard of it, list that imperfection is perfect. It applies not only to human affairs, but to technology. Thus, irregularity in semiconductor crystals (an imperfection, in the form of contaminants) is requisite for the production of semiconductors. The solution to the apparent paradox lies in a distinction between two concepts of "perfection": that of regularity, and that of utility. Imperfection is perfect in technology, in the sense that irregularity is useful. Source: http://en.wikipedia.org... Now I must consider your questions: If work must be done to fix the result, the result is not wrong prior to the fix, because work must be done to create the system in the first place. There are no systems that you would not consider them to be "flawed", by your definition of flaw. Now if I multiply 1/3 by 3, I would get 1. 3* 1/3 = 1 Now if I divide 1 by 3, I would get 0.999… But don't you know that 0.999… = 1 In case you didn't know, In mathematics, the recurring decimal 0.999… denotes a real number equal to 1. In other words, the notations "0.999…" and "1" represent the same real number. The equality has long been accepted by professional mathematicians and taught in textbooks. Various proofs of this identity have been formulated with varying rigour, preferred development of the real numbers, background assumptions, historical context, and target audience. Proof: 1. Multiplication of 3 times 3 produces 9 in each digit, so 3 � 0.333… equals 0.999…. And 3 � 1⁄3 equals 1, so 0.999… = 1. 2. 1 = 9/9 = 9 x 1/9 = 9 x 0.111... = 0.999... Since both equations are valid, by the transitive property, 0.999… must equal 1. Similarly, 3/3 = 1, and 3/3 = 0.999…. So, 0.999… must equal 1. In case you want more proof, go to http://en.wikipedia.org... IEEE 7541985 is the most widelyused standard for floatingpoint computation, and is followed by many CPU and FPU implementations. It has 4 rounding modes. Did you know that The IEEE floating point standard must round because the result of operations on floating point numbers are not always representable because of limitations in precision? So you call it as flawed? Nothing is perfect and will always need perfection. Source: http://en.wikipedia.org... I agree with you the fact that crossplatform has problems. However, there are different ways of approaching the problem of writing a crossplatform application program. One such approach is simply to create multiple versions of the same program in different source trees—in other words, the Windows version of a program might have one set of source code files and the Macintosh version might have another, while a FOSS *nix system might have another. While this is a straightforward approach to the problem, it has the potential to be considerably more expensive in development cost, development time, or both, especially for the corporate entities. The idea behind this is to create more than two different programs that have the ability to behave similarly to each other. It is also possible that this means of developing a crossplatform application will result in more problems with bug tracking and fixing, because the two different source trees would have different programmers, and thus different defects in each version. The smaller the programming team, the quicker the bug fixes tend to be. Another approach that is used is to depend on preexisting software that hides the differences between the platforms—called abstraction of the platform—such that the program itself is unaware of the platform it is running on. It could be said that such programs are platform agnostic. Programs that run on the Java Virtual Machine (JVM) are built in this fashion. Some applications mix various methods of crossplatform programming to create the final application. An example of this is the Firefox web browser, which uses abstraction to build some of the lowerlevel components, separate source subtrees for implementing platform specific features (like the GUI), and the implementation of more than one scripting language to help facilitate ease of portability. Firefox implements XUL, CSS and JavaScript for extending the browser, in addition to classic Netscapestyle browser plugins. Much of the browser itself is written in XUL, CSS, and JavaScript, as well. Source:http://en.wikipedia.org... Therefore, the rounding system is still not flawed just because of potential problems of crossplatform programming. I said "But the REAL problem was not with inaccuracy, but with inconsistency" Rounding causes problem with inaccuracy, but not with inconsistency. During one of the updates, Raytheon Labs, the developer of the patriot missile, had fixed the previously mentioned inaccuracy problem by creating code that used a pair of 24 bit registers to accurately make the time calculations. The problem was that that most, but not all of the time calculations made by the system were replaced by calls to the newer, more accurate function. So, the system was keeping track of the current time using a function that loses time in much the same way that a clock with a weak battery will gradually lose time. But, the system would track missiles, aim itself, and decide exactly when to launch it's own missiles using the internal clock, which was accurate. In effect, the system would use an accurate timepiece to decide where the missile is located and how fast it is moving, and when to fire the defensive missiles. But while waiting to fire the missiles, the system would use the less accurate clock to determine when it should fire. As you can see, rounding does not cause the problem with the Patriot Missile System. There are errors so small that we don't even notice it if our genes contain the slightest amount of error that it doesn't count toward genetic diseases. Only the major, more noticeable changes of genes would cause genetic disorders. DNA repair mechanisms are able to mend most changes before they become permanent mutations, and many organisms have mechanisms for eliminating otherwise permanently mutated somatic cells. Therefore, we don't have flawed genes or DNA, otherwise we would be doomed. I conclude that the decimal/metric system with rounding is not flawed. Maybe it is imperfect, but it could be improved; just like everything else. I apologize that I can't post the next argument sooner due to school and sleep with homework involved. Thank you and good luck! 

Thank you for your reply and your brilliant answers.
1.) I like the perfection/imperfection details. Absolutely, But... A.) Your original argument stated "Rounding exist for these reasons:1. Speed of computation 2. Ease of computation" B.) Your following arguments indicate an understanding that work must be done to fix results. C.) Do you not see the irony of what you say? For ease and speed, yet you must WORK hard to fix it. D.) Does it not defeat the purpose of "ease" if takes a "rocket scientist" to get results with minimal accuracy? E.) Don't you think the average intellect that does not how to fix it as you do will have problems with a system that is supposed to be...well... easy? 2.) You Said "But don't you know that 0.999… = 1" Sorry, but I have to disagree. 0.999... and other "run on numbers" are NOT numbers until you STOP working(multiplying or dividing), They are FUNCTIONS. It is a function with no time step limit, converging on 1.0, but NEVER reaching it. A "Black Hole" of a time sink that will suck up resources and work unless it is stopped. If that function is "set in motion" it will continue for ever and never reach 1.0. as long as you keep working. When you stop working you must either truncate or round. i.e .999  work + round = 1 The instant you stop working, the function becomes a number. THAT number is not always the right number. When we prevent this inaccuracy by not dividing into a prime and leave the function as is, we wind up with fractions. And fractions are not succeptable to this rounding flaw... until you divide. A good debate to start would be: which is better "metric", "english", or something that maybe uses BOTH. Besides, 1/2 a cup of cofee is easier to use and sounds better than 367.345 milli liters. 3.) You were right on the Tracking system. "Your honor, it was hearsay and was inadmissable." You got me. It wasn't a good example. 4.) You Said "Therefore, the rounding system is still not flawed just because of potential problems of crossplatform programming." It did not say "just because", I said "The rounding error in computers (OMG!!! you didn't go there) is further proof of the flaw we discuss."  more evidence indicating the flaw/error/problem and complicating ease of use. 5.) You Said " You said "But the REAL problem was not with inaccuracy, but with inconsistency" Rounding causes problem with inaccuracy, but not with inconsistency." I have to argue this point as well. The rounding function adds random and chaotic behavior to iterative and recursive functions. DID you not check my research? LOOK at the graph, It's all over the place. If it were "consistent" it's behavior would not be chaotic and random. If it were "consistent" it would be predictable. If it were "consistent" the flaw could be removed from the system. The flaw is not only inaccuracy, but inconsistency. The only conditions for consistency, are when you use the same set of number/operations in the SAME order. There is NO consistency across differnt number sets of the same operations. Fractals take advantage of this principle. We wouldn't have fractals but for the decimal system. Many functions intentionally exagerate this error to intoduce "chaotic" behavior to systems modeling reality. BUT! This flaw is not benign, soft spoken, nor polite as you describe it... It is elusive, chaotic, and inaccurate and one of the most beautiful flaws I have ever known. I Understand your love of it, I love it as well, but it is not the secrets of the universe, just a very useful tool. A tool that if we do not acknowledge it's flaws and imperfections and try to understand it, will prevent us from finding something better. I for one am not willing to sacrifice the Stars because my love for the decimal and metric systems refuses to let me seek an alternative. I surely won't give up my EASY flawed English system with its fractions for something I KNOW to be flawed as well. BUT, I will use both of them until something better comes along. Still, Flaws are Flaws are Flaws and Imperfections. Lets call this dog a dog and admit it has fleas. I still love the dog and it is not nearly time to put him to sleep... yet. I say admit the flaws with the decimal/metric system by voting PRO for my position.
Thank you for replying. I will counter your contentions as well as bring up other points. I realize that I should make myself more understandable and clear. A. My original argument stated that rounding exist for these reasons: 1. Speed of computation 2. Ease of computation I should go deeper and explain more: In computers and calculators, these methods are used for one of two reasons: speed of computation or usefulness in certain computer algorithms. Speed of computation and ease of computation introduce more roundoff error and therefore are rarely used in statistics and science; they are still used in computer algorithms because they are slightly easier and faster to compute. But you said in your Round 2 "I concede your point that it works fine for single stage equations such as averages, conversions, statistics, etc." Therefore, it doesn't take a "rocket scientist" to work with the metric system to get minimal accuracy if they are working with elementary calculus and mathematics in school. Then you said also in Round 2 "the margin of error introduced by rounding increases with the time complexity of the problem and is exaggerated through feedback and amplification. This accumulated error over time make the decimal/metric systems with rounding flawed. This flaw or amount of error is measurable." So you're talking about things much more sophisticated and complicated than elementary calculus and mathematics. Therefore, I should revise and say that rounding before college exist for the speed and ease for computation. B. What about rounding after college and in computers? Well, squeezing infinitely many real numbers into a finite number of bits into the computer requires an approximate representation. Although there are infinitely many integers, in most programs the result of integer computations can be stored in 32 bits. In contrast, given any fixed number of bits, most calculations with real numbers will produce quantities that cannot be exactly represented using that many bits. Therefore the result of a floatingpoint calculation must often be rounded in order to fit back into its finite representation. This rounding error is the characteristic feature of floatingpoint computation. That is why rounding exist. Since most floatingpoint calculations have rounding error anyway, does it matter if the basic arithmetic operations introduce a little bit more rounding error than necessary? I shall go back to guard digits. Guard digits were considered sufficiently important by IBM that in 1968 it added a guard digit to the double precision format in the System/360 architecture (single precision already had a guard digit), and retrofitted all existing machines in the field. Of course I can't provide the proof of guard digits because the maximum number of characters allowed is 8,000. But you can see the proof of guard digits here: http://docs.sun.com... It is not uncommon for computer system designers to neglect the parts of a system related to floatingpoint. This is probably due to the fact that floatingpoint is given very little (if any) attention in the computer science curriculum. This in turn has caused the apparently widespread belief that floatingpoint is not a quantifiable subject, and so there is little point in fussing over the details of hardware and software that deal with it. The website http://docs.sun.com... has demonstrated that it is possible to reason rigorously about floatingpoint. For example, floatingpoint algorithms involving cancellation can be proven to have small relative errors if the underlying hardware has a guard digit, and there is an efficient algorithm for binarydecimal conversion that can be proven to be invertible, provided that extended precision is supported. The task of constructing reliable floatingpoint software is made much easier when the underlying computer system is supportive of floatingpoint. Rounding must exist, because there are lots of numbers that can't represented by 32 bits. That is also another reason why the metric system is not garbage. It's the computers that can't store infinitely many real numbers that cause the existence of rounding. C. In mathematics, the recurring decimal 0.999… denotes a real number equal to 1. There are two debates about this and the pros always win: http://www.debate.org... http://www.debate.org... Pros always win those debates because the equality has long been accepted by professional mathematicians and taught in textbooks. Various proofs of this identity have been formulated with varying rigour, preferred development of the real numbers, background assumptions, historical context, and target audience. I agree that a good debate to start would be: Metric System versus U.S units. D. On February 25th, 1991, a Patriot Missile system that had been running for over 100 hours at Dhahran, Saudi Arabia had failed to intercept a SCUD missile. The SCUD hit an Army Barracks, killing 28 Americans. On the next day, the Bug Fix for the system arrived at Dhahran. The reason this bug occurred is because of a problem with storing time in a 24bit register. The problem is that time is stored to an accuracy of 1/10th of a second, but a 24bit register does not have enough precision to store 0.1, so a small fraction of each second is lost. The result is that the register used to keep track of time is off by 0.0001% of the amount of time that the system has been in operation. The problem is that computers do not store information as a standard decimal. Instead, they use binary code, which can not accurately store 1/10th of a second. It's the computer's limitations of having finite bits that result in inaccuracy and inconsistency. E: Now I must explain why the metric system existed in the first place. The metric system was designed with several goals in mind: 1. Neutral and Universal: the designers of the metric system meant to make it as neutral as possible so that it could be adopted universally. 2. Replicable: the usual way to establish a standard was to make prototypes of the base units and distribute copies. This would make the new standard reliant on the original prototypes which would be in conflict with the previous goal since all countries would have to refer to the one holding the prototypes. The designers developed definitions of the base units such that any laboratory equipped with proper instruments should be able to make their own models of them. The original base units of the metric system could be derived from the length of a meridian of the Earth and the weight of a certain volume of pure water. They discarded the use of a pendulum since its period or, inversely, the length of the string holding the bob for the same period changes around the Earth. Likewise, they discarded using the circumference of the Earth over the Equator since not all countries have access to the Equator while all countries have access to a section of a meridian. 3. Decimal multiples: the metric system is decimal, in the sense that all multiples and sub multiples of the base units are factors of powers of ten of the unit. Fractions of a unit are not used formally. The practical benefits of a decimal system are such that it has been used to replace other nondecimal systems outside the metric system of measurements; for example currencies. Source: http://en.wikipedia.org... And these goals doesn't NOT include creating a perfect international system that can't be improved as long as humanity lives. Therefore it is not garbage because it can be used internationally and scientifically and is not limited to one country, like the U.S. units system. One cup of coffee may sound good to Americans, but in Europe, one liter of coffee sounds a lot better. 

Thank you for your time and energy on this debate.
To address Point A of round 4, I would have to say in response that NO, I am not talking about JUST advanced calculations involving rounding. Even Simple Ones. The example and research of round 1 shows that the decimal system with rounding cannot handle simple distributive type problems such as Sum(Item Price)* Markup% <> Sum(Item Price * Markup%) For the decimal and metric systems to be practical in real world applications. They should be distributable such that A * (X + Y) = AX + AY but they do not. Because of rounding, functions that should be equal and that use the decimal system are NOT. I will proof that using the decimal system with rounding means that indeed Sum(Item Price)* Markup% <> Sum(Item Price * Markup%) I should be able to take Sum(Item Price) * Markup% and distribute Markup% accross the Sum(Item Price) which is in effect (item[1].price + item[2].price + ... + item[n].price) This is a simple financial type transaction involving a decimal currency. We're going to go outside the class room and into the real world with this example. You are given the apparently simple task of splitting up the total of a retail order by class for the reporting the class total and correct item amount of each item to some financial agency. class 1 will be NOT class 2 will be IS You are given: 100 random items of random class in the range 0 thru 9.99 You are given: You are given a random Markup% in the range 1.00 thru 20.00 You are given: The total of the order as Sum(items) * Markup% Your function must process the list of items and tell me the correct amount to report to the financial agency for all items marked class 2 "IS". Your function MUST deliver the right answer. One not understanding this issue would think that (Sum(Class 1 Price)* Markup%) + (Sum(Class 2 Price)* Markup%) should equal Sum(Item Price) * Markup% One not understanding the flaw inherint in rounding would assume that he could distribute markup percent to each item. Stage1: Sum(Item Price) * Markup% Stage2: (item[1].price + item[2].price + ... + item[n].price) * Markup% Stage3: ((item[1].price * Markup%)+ (item[2].price * Markup%) + ... + (item[n].price * Markup%)) Pretty standard stuff so far, any average man would assume that the metric system was distributable just as we were taught. Here are your data sets Data Set 1 ItemPrice = 1.37,3.91,8.79,10.91,9.27,9.03,8,10.28,6.83,6.69,5.09,7.84,8.08,4.18,2.89,5.87,9.53,1.91,5.64,0.42,0.89,5.54,7.62,5.33,10.74,7.51,2.92,3.08,4.39,2.77,3.69,5.09,4.36,9.63,8.12,1.58,6.53,5.06,1.99,6.87,1.27,6.56,10.19,1.79,9.18,4.66,10.06,4.79,6.84,8.47,0.82,6.4,8.4,4.9,1.37,9.82,1.61,8.24,1,5.46,9.24,2.29,9.22,8.47,3.87,9.59,5.29,2.31,6.22,0.79,8.99,4.66,0.14,7.5,2.38,5.89,1.38,9.01,8.93,0.46,9.43,6.15,6.36,9.26,2.67,7.94,9.12,7.04,0.22,10.44,7.11,2.75,7.09,0.98,1.19,1.69,2.54,6.74,9.8 Markup = 19% Order Total without Markup = 557.22 Markup Amount = 105.87 ******* Order Total with Markup = 663.09 ItemAmount(Item Price + (ItemPrice*Markup%)) = 1.63,4.65,10.46,12.98,11.03,10.75,9.52,12.23,8.13,7.96,6.06,9.33,9.62,4.97,3.44,6.99,11.34,2.27,6.71,0.5,1.06,6.59,9.07,6.34,12.78,8.94,3.47,3.67,5.22,3.3,4.39,6.06,5.19,11.46,9.66,1.88,7.77,6.02,2.37,8.18,1.51,7.81,12.13,2.13,10.92,5.55,11.97,5.7,8.14,10.08,0.98,7.62,10,5.83,1.63,11.69,1.92,9.81,1.19,6.5,11,2.73,10.97,10.08,4.61,11.41,6.3,2.75,7.4,0.94,10.7,5.55,0.17,8.93,2.83,7.01,1.64,10.72,10.63,0.55,11.22,7.32,7.57,11.02,3.18,9.45,10.85,8.38,0.26,12.42,8.46,3.27,8.44,1.17,1.42,2.01,3.02,8.02,11.66 ******* ItemAmountTotal = 663.16 Accumulated Error Between our two functions = 0.0682 or 0.07 7 cents off using rounding. I can give you thousands of datasets that prove the decimal system is not even distributable except under ideal or classroom conditions. You can't give me one function using rounding that will handle all possible datasets. Every fix you can name for the rounding error doesn't fix it, but only minimizes it for a particular application. Every fix you can come up with will have a dataset that breaks it. Every fix you can come up with will eventually produce a number of wrong anwers If we fully develop all the possible scenarios for using the decimal system, we will have explored each and every way to fix it. B.) About rounding after college in computers?  I wish we had time to talk about it, as you and i both agree it is facinating and a problem with a multitude of different types of "fixes".  The problem is we have limited time and as mathematical rounding errors and decimal conversion are the cause of computer rounding errors... well we're debating general and this complicates the issue for potential voters.  The issue is if the error is a flaw(which you admit) and just how bad is the flaw. C) ".9999 = 1.0" Lets look at this for a sec. Is this a natural law, a standard, or a peer agreement  In the case of natural law, i would have to say false as it cannot be created without rounding and work and value has specific meaning. It is subject to the law "if an object is set in motion it will continue forever until stopped." to hide the rounding is lazy and irresponsible.  In the case of a standard, i would have to say true. If enough people use it that way, then that is what the two symbols mean to them. This does Not however mean it is true about the VALUES of those symbols, just the USE.  In the case of a peer agreement, i would have say true as well. Still this is true only in peer group and in the context of the use of those symbols, not the reality of the value of those symbols. However, this is a debate for another forum. Lets Move On and stick the topic. D.) You said again "It's the computer's limitations of having finite bits that result in inaccuracy and inconsistency" No, the decimal system with rounding already has an error that both you and I have identified and acknowledged. The error in the decimal system came first, and is the CAUSE of the floating point errors in computers. Floating Point Arithmatic has problems with the decimal system, because it cannot be used without rounding except in ideal instances. The complexity of the rounding error is such that no two processor manufacturers round the same way. The sheer number of fixes is evidence to the complexity, the inaccuracy, and the inconsistency of this error that you feel is not small enough to consider it NOT a flaw. E.) You didn't need to, as you already have expressed it's usefullness. I myself have indicated that I use it and love it. Please read back and you will note this. The reason for using the metric system IS NOT applicable to this debate. I can't argue against it as I use it. The debate is if the decimal/metric system is flawed or not and we've since added debate over the magnitude of this flaw. We know the cause of this flaw, and it is because of rounding. We both agree on that. We know it has problems accross the board, but people have a hard time admitting it. It's a very emotional argument. But, Science is about the search for truth. About experimenting and about results. The evidence indicates the flaw. The opposition has presented evidence for minimizing the flaw that are application specific. The sheer number of types of fixes is evidence that the flaw is a lot bigger than you would make it seem. It's supposed to be easy and we've proven it is not. In conclusion, I would like to thank you for presenting the opposite side. It's been fun, and I've leaned a lot. The research and evidence is in round 1. My opponent graciously conceeded later, that the error is indeed a flaw. He position since has been "nothing is perfect", "i like the metric system", "it's not really that big of an error." Stand up for the TRUTH!!! It's Flawed
First of all, my opponent states the problem of A * (X + Y) = AX + AY. In this problem, he only use the common method of rounding and uses no guard digits or any other technique to minimize the magnitude of rounding errors. To minimize the accumulated error, Roundtoeven method is used. A. This method is also known as unbiased rounding, convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, or bankers' rounding. It is identical to the common method of rounding except when the digit(s) following the rounding digit starts with a five and has no nonzero digits after it. The new algorithm is: * Decide which is the last digit to keep. * Increase it by 1 if the next digit is 6 or more, or a 5 followed by one or more nonzero digits. * Leave it the same if the next digit is 4 or less * Otherwise, if all that follows the last digit is a 5 and possibly trailing zeroes; then change the last digit to the nearest even digit. That is, increase the rounded digit if it is currently odd; leave it if it is already even. With all rounding schemes there are two possible outcomes: increasing the rounding digit by one or leaving it alone. With traditional rounding, if the number has a value less than the halfway mark between the possible outcomes, it is rounded down; if the number has a value exactly halfway or greater than halfway between the possible outcomes, it is rounded up. The roundtoeven method is the same except that numbers exactly halfway between the possible outcomes are sometimes rounded up—sometimes down. Although it is customary to round the number 4.5 up to 5, in fact 4.5 is no nearer to 5 than it is to 4 (it is 0.5 away from both). When dealing with large sets of scientific or statistical data, where trends are important, traditional rounding on average biases the data upwards slightly. Over a large set of data, or when many subsequent rounding operations are performed as in digital signal processing, the roundtoeven rule tends to reduce the total rounding error, with (on average) an equal portion of numbers rounding up as rounding down. This generally reduces upwards skewing of the result. Roundtoeven is used rather than roundtoodd as it reduces rounding to a final digit of 5, and so reduces the likelihood of error resulting from double rounding. Source: http://en.wikipedia.org... My opponent did not used this method so he got an accumulated error of 7 cents of the common method of rounding. If you use the roundingtoeven method, you would find that be a lot less than 7 cents. Unfortunately, I can't show you that, because only 8,000 characters are allowed. But you can try and find out in your free time. The roundingtoeven method can handle large sets of scientific or statistical data and will minimize the magnitude of rounding errors. My opponents thinks that I can't give him one function using rounding that will handle all possible data sets. In truth, no one can came up with a function using rounding that is perfect, because nothing is perfect. Rounding is the process of reducing the number of significant digits in a number. The result of rounding is a "shorter" number having fewer nonzero digits yet similar in magnitude. The result is less precise but easier to use. Therefore, rounding will make ALL functions include errors. So, someday, you can make a system better than metric, but when you include rounding, it WILL have errors. In conclusion, the future system with rounding is nothing better than the metric system with rounding. B. My opponent thinks that mathematical rounding errors and decimal conversion are the cause of computer rounding errors. However, I disagree. Floatingpoint numbers are represented in computer hardware as base 2 (binary) fractions. For example, the decimal fraction 0.125 has value 1/10 + 2/100 + 5/1000, and in the same way the binary fraction 0.001 has value 0/2 + 0/4 + 1/8. These two fractions have identical values, the only real difference being that the first is written in base 10 fractional notation, and the second in base 2. Unfortunately, most decimal fractions cannot be represented exactly as binary fractions. A consequence is that, in general, the decimal floatingpoint numbers you enter are only approximated by the binary floatingpoint numbers actually stored in the machine. No matter how many base 2 digits you're willing to use, the decimal value 0.1 cannot be represented exactly as a base 2 fraction. In base 2, 1/10 is the infinitely repeating fraction 0.0001100110011001100110011001100110011001100110011... Stop at any finite number of bits, and you get an approximation. This is why you see things like: >>> 0.1 0.10000000000000001 On most machines today, that is what you'll see if you enter 0.1 at a Python prompt. You may not, though, because the number of bits used by the hardware to store floatingpoint values can vary across machines, and Python only prints a decimal approximation to the true decimal value of the binary approximation stored by the machine. On most machines, if Python were to print the true decimal value of the binary approximation stored for 0.1, it would have to display >>> 0.1 0.1000000000000000055511151231257827021181583404541015625 Note that this is in the very nature of binary floatingpoint: this is not a bug in Python, and it is not a bug in your code either. You'll see the same kind of thing in all languages that support your hardware's floatingpoint arithmetic (although some languages may not display the difference by default, or in all output modes). The errors in Python float operations are inherited from the floatingpoint hardware, and on most machines are on the order of no more than 1 part in 2**53 per operation. That's more than adequate for most tasks, but you do need to keep in mind that it's not decimal arithmetic, and that every float operation can suffer a new rounding error. While pathological cases do exist, for most casual use of floatingpoint arithmetic you'll see the result you expect in the end if you simply round the display of your final results to the number of decimal digits you expect. Therefore, you can infer that binary number system is the cause of rounding and rounding errors in computers. Source: http://www.python.org... C. 0.9999... (NOT 0.9999 as my opponent put) =1.0 This is a natural law, standard, and peer agreement as proven by various proofs written by many mathematicians. My opponent has misinterpreting the meaning of the use of the "…" (ellipsis) in 0.999… accounts for some of the misunderstanding about its equality to 1. The use here is different from the usage in language or in 0.99…9, in which the ellipsis specifies that some finite portion is left unstated or otherwise omitted. When used to specify a recurring decimal, "…" means that some infinite portion is left unstated, which can only be interpreted as a number by using the mathematical concept of limits. As a result, in conventional mathematical usage, the value assigned to the notation "0.999…" is the real number which is the limit of the convergent sequence (0.9, 0.99, 0.999, 0.9999, …). But I can't elaborate more since I'm almost out of characters. Source: http://en.wikipedia.org... D. The same thing I would say for point B. I would put the source that elaborate my point such as the rounding problem in Excel that my opponent put in his first argument: http://support.microsoft.com... In conclusion, the reason I said that rounding is not garbage is because our computers are not advance enough to store infinite numbers in a finite number of bits. Therefore, the computers has flaws, NOT the metric system. I would like to point out that my opponent did not even use sources to prove his point. Therefore, I highly urge you to vote for CON as it is the truth that the metric system isn't garbage. 
11 votes have been placed for this debate. Showing 1 through 10 records.
Vote Placed by arthurxanimal 8 years ago
RantNRave31  Dnick94  Tied  

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Vote Placed by Rezzealaux 9 years ago
RantNRave31  Dnick94  Tied  

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Vote Placed by JBlake 9 years ago
RantNRave31  Dnick94  Tied  

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Vote Placed by PoeJoe 9 years ago
RantNRave31  Dnick94  Tied  

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Vote Placed by brittwaller 9 years ago
RantNRave31  Dnick94  Tied  

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Vote Placed by Robert_Santurri 9 years ago
RantNRave31  Dnick94  Tied  

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Vote Placed by Kleptin 9 years ago
RantNRave31  Dnick94  Tied  

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Vote Placed by benj 9 years ago
RantNRave31  Dnick94  Tied  

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Vote Placed by Wayne 9 years ago
RantNRave31  Dnick94  Tied  

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Vote Placed by zantilley 9 years ago
RantNRave31  Dnick94  Tied  

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Con could have easily denied Pro's attempt to redefine the resolution yet con did not. Con's retorhical questions do nothing to oppose Pro's new resolution; "Metric Rounding has Flaws." Instating the 'paradox of perfection' was an interesting approach but was hardly justified.
R4
From here the arguments breaks down to Pro saying there are still flaws and Con saying the flaws and minimal and fixable or benign. R5 is just specifics. None of Con's arguments convinced me that Metric Rounding is Flawless.
Prognosis:
Agreed with Con Before.
Agreed with Con After.
Conduct >Con, Both parties had good conduct yet Con had slightly better
Spll/Grm.> Con
Arguments > Tie. since Pro changed the resolution and Con accpeted it.
Sources > Con
Resolution The Metric System with Rounding is Garbage which, since it wasn't specified I must take to mean The Metric System with Rounding should be done away with, or shouldn't be used.
R1
Pro's argument was unclear and not precise. He gives many specific yet very unclear examples which makes me skeptical. His argument follows: Rounding with the metric system has flaws. Therefore it shouldn't be used.  He failed to provide an alternate system that works more effectively and since we clearly cannot throw out mathematics in general i am not convinced by his arguments.
Con very clearly and concisely explained the usefulness of rounding with the metric system.
R2
Pro begins by arguing that although rounding is useful it allows for error, therefore it shouldn't be used. This is an inherently illogical stance because something which is useful should be used by definition. He then tries to adjust his initial resolution *which he never actually made clear* to being only about compound rounding errors claiming that "Simple equations do not suffer from compound rounding errors and therefore are not applicable to this debate." That was never explicitly clarified beforehand and the resolution cannot be adjusted in R2. He then makes claims about irrational numbers which may be true. But there is no source to validate the truth or falsity of these claims so that argument isn't overwhelmingly convincing either. Con clearly addresses the issues posed.
R3
Although pro isn't doing a bad job he has chosen a very difficult resolution. Pro argues that there are still errors and restates his initial argument about flaws, yet seems unaware that his resolution was about the utility of metric rounding, not simply that it can have errors. (something that is garbage is something that should be done away with. i.e. something that is not useful.) However, Because Con has chosen to accept this adjusted resolution i must allow it.
 While both sides indeed remained extremely courteous, Pro attempted to alter his resolution in the middle of the debate.
Spelling/Grammar: Tie
 A small number of mistakes on both sides, but nothing of great consequence. They were both clear in their arguments.
Convincing Argument: Con
 Con showed that while there will certainly be flaws, the current system keeps them at a minimum. Based on his R1, Pro needed to show that the system should be scrapped (as shown by the following statement in R1 "Why should we use the metric system with it's inherent flaws"), this he did not do.
Sources: Con
 Pro provided no sources while Con provided plenty.
To my fellow cleaners, if you have firefox, download the "Web Developer" addon. With it, I was able to edit the html locally to make it much easier to read.
Conduct  TIED  Both debaters made the effort to thank and compliment each other. No personal attacks.
Spelling and grammar  TIED  A quick copy+paste into Microsoft Word shows both debaters made minor errors. Nothing substantial though.
Convincing arguments  CON  PRO changed the resolution as to make CON's case impossible. Also, I liked CON'S point that it was the limitation of computers, not the metric system itself that was the problem.
Reliable sources  CON  I think this is pretty obvious. CON even pointed out his opponent's lack of sources.
I learned a few things here, which is nice. I also greatly appreciate both debaters' use of detail and their understanding of the subject matter. Still, a nightmare to read;)
Conduct: Tied. Both were respectful.
Spelling and Grammar: Tied. There were mistakes by both PRO and CON, so it evens out.
Arguments: CON. PRO changed his resolution to "The metric system with rounding is imperfect" in the middle of the debate, which is unacceptable. There is 1) no debate as to whether any system of rounding is flawed, i.e. imperfect  it goes without saying and 2) in regard to the original resolution, which I am judging by, CON easily showed that although rounding is flawed, there are ways to minimize error, and even if these methods are also flawed, nothing is perfect and never will be. PRO did not prove, or even try to prove, as his resolution changed, that "the metric system with rounding is garbage," or should be discarded. A very long road to a rather short and easy win for CON.
Sources: CON. This is selfevident.
Britt
I agree with LR and Kleptin that this was a bit of hell to read at times but I thought it was also a bit interesting.
Conduct: Tie
Both sides were polite and respectful. Neither side insulted the other or along the lines of that.
Spelling and Grammar: Tie
Both sides organized their arguments well and had their share of errors. The formatting error was a bit of a problem in my honest opinion.
Arguments: Dnick94
There is a difference between flawed and garbage. Nothing is perfect and this debate wasn't about how the Metric System was/was not perfect. Rather that it was garbage. CON showed several points that the Metric System has it's uses and quite efficient at times.
Sources: Dnick94
PRO cited one source for this difficult debate while CON sourced many during his debate and at the end. I was able to research more of the topic and understand it quite better thanks to CON's sources. CON gets these points.
I concur with Kleptin, this was hell to read. Hell. Mostly due to the formatting issues, but nonetheless, it was bad.
Conduct: Tie
Both sides were polite and respectful.
Spelling and Grammar: Tie
Both sides had some errors, so it all balanced out.
Arguments: Dnick94
Dnick showed us that the metric system, although flawed was useful and efficient.
Sources: Dnick94
Lots of good sources on his side.
So, with a vote of 40, Dnick94 is the winner!
@.@ This was an unpleasant debate to have to read all the way through, I did not enjoy it, but for the sake of debate.org and my duty as a cleaner, I did >.>
Conduct I tied this category. Both sides made attempts to show adequate conduct, which is enough. Most of it did not sound sincere and I understood that both sides were rushing to get to the crux of the matter.
Spelling and grammar Also a tie. The complicated nature of this debate, as well as the unfortunate formatting error makes it near unreadable to someone looking for an interesting debate...however, both sides organized their arguments quite well, and were fair in spelling and grammar.
Arguments Both sides made adequate arguments, and in terms of factual knowledge, I, having little to no experience on the matter, would tie the points. However, PRO's argument that CON admitted the metric system to have flaws was a poor one. The resolution is not that the metric system is flawless, but that the metric system is GARBAGE. And garbage, is something that needs to be discarded. The burden of proof, in this case, falls on PRO to prove that the metric system should be discarded. Since he has failed to do so, and CON has given arguments as to why it should be kept, and also since PRO himself has admitted it should not be thrown away, the argument points go OBJECTIVELY to CON.
Sources PRO cited one source, whereas CON's argument was flooded with the proper source citations for many difficult terms and concepts. This makes the debate easy to research and understand. Points go to CON.