The Metric System with Rounding is Garbage

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 round-off 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 floating-point calculation must often be rounded in order to fit back into its finite representation. This rounding error is the characteristic feature of floating-point computation. That is why rounding exist. Since most floating-point 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 floating-point. This is probably due to the fact that floating-point is given very little (if any) attention in the computer science curriculum. This in turn has caused the apparently widespread belief that floating-point 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 floating-point. For example, floating-point 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 binary-decimal conversion that can be proven to be invertible, provided that extended precision is supported. The task of constructing reliable floating-point software is made much easier when the underlying computer system is supportive of floating-point. 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 24-bit register. The problem is that time is stored to an accuracy of 1/10th of a second, but a 24-bit 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 non-decimal 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.