1.
Scientific notation
–
Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations, on scientific calculators it is known as SCI display mode. In scientific notation all numbers are written in the form m × 10n, where the exponent n is an integer, however, the term mantissa may cause confusion because it is the name of the fractional part of the common logarithm. If the number is then a minus sign precedes m. In normalized notation, the exponent is chosen so that the value of the coefficient is at least one. Decimal floating point is an arithmetic system closely related to scientific notation. Any given integer can be written in the form m×10^n in many ways, in normalized scientific notation, the exponent n is chosen so that the absolute value of m remains at least one but less than ten. Thus 350 is written as 3. 5×102 and this form allows easy comparison of numbers, as the exponent n gives the numbers order of magnitude. In normalized notation, the exponent n is negative for a number with absolute value between 0 and 1, the 10 and exponent are often omitted when the exponent is 0. Normalized scientific form is the form of expression of large numbers in many fields, unless an unnormalized form. Normalized scientific notation is often called exponential notation—although the latter term is general and also applies when m is not restricted to the range 1 to 10. Engineering notation differs from normalized scientific notation in that the exponent n is restricted to multiples of 3, consequently, the absolute value of m is in the range 1 ≤ |m| <1000, rather than 1 ≤ |m| <10. Though similar in concept, engineering notation is rarely called scientific notation, engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication. A significant figure is a digit in a number that adds to its precision and this includes all nonzero numbers, zeroes between significant digits, and zeroes indicated to be significant. Leading and trailing zeroes are not significant because they exist only to show the scale of the number. Therefore,1,230,400 usually has five significant figures,1,2,3,0, and 4, when a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the place holding zeroes are no longer required, thus 1,230,400 would become 1.2304 ×106. However, there is also the possibility that the number may be known to six or more significant figures, thus, an additional advantage of scientific notation is that the number of significant figures is clearer
2.
Metric prefix
–
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in use today are decadic, historically there have been a number of binary metric prefixes as well. Each prefix has a symbol that is prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand, the prefix milli-, likewise, may be added to metre to indicate division by one thousand, one millimetre is equal to one thousandth of a metre. Decimal multiplicative prefixes have been a feature of all forms of the system with six dating back to the systems introduction in the 1790s. Metric prefixes have even been prepended to non-metric units, the SI prefixes are standardized for use in the International System of Units by the International Bureau of Weights and Measures in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities, the BIPM specifies twenty prefixes for the International System of Units. Each prefix name has a symbol which is used in combination with the symbols for units of measure. For example, the symbol for kilo- is k, and is used to produce km, kg, and kW, which are the SI symbols for kilometre, kilogram, prefixes corresponding to an integer power of one thousand are generally preferred. Hence 100 m is preferred over 1 hm or 10 dam, the prefixes hecto, deca, deci, and centi are commonly used for everyday purposes, and the centimetre is especially common. However, some building codes require that the millimetre be used in preference to the centimetre, because use of centimetres leads to extensive usage of decimal points. Prefixes may not be used in combination and this also applies to mass, for which the SI base unit already contains a prefix. For example, milligram is used instead of microkilogram, in the arithmetic of measurements having units, the units are treated as multiplicative factors to values. If they have prefixes, all but one of the prefixes must be expanded to their numeric multiplier,1 km2 means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres. 2 Mm3 means two cubic megametres, or the volume of two cubes of 1000000 m by 1000000 m by 1000000 m or 2×1018 m3, and not 2000000 cubic metres, examples 5 cm = 5×10−2 m =5 ×0.01 m =0. The prefixes, including those introduced after 1960, are used with any metric unit, metric prefixes may also be used with non-metric units. The choice of prefixes with a unit is usually dictated by convenience of use. Unit prefixes for amounts that are larger or smaller than those actually encountered are seldom used
3.
Frequency counter
–
A frequency counter is an electronic instrument, or component of one, that is used for measuring frequency. Frequency counters usually measure the number of oscillations or pulses per second in an electronic signal. Such an instrument is referred to as a cymometer, particularly one of Chinese manufacture. Most frequency counters work by using a counter which accumulates the number of events occurring within a period of time. After a preset period known as the time, the value in the counter is transferred to a display. The internal oscillator which provides the signals is called the timebase. If the event to be counted is already in electronic form, more complex signals may need some conditioning to make them suitable for counting. Most general purpose frequency counters will include some form of amplifier, DSP technology, sensitivity control and hysteresis are other techniques to improve performance. Other types of events that are not inherently electronic in nature will need to be converted using some form of transducer. For example, an event could be arranged to interrupt a light beam. Frequency counters designed for radio frequencies are also common and operate on the principles as lower frequency counters. Often, they have more range before they overflow, for very high frequencies, many designs use a high-speed prescaler to bring the signal frequency down to a point where normal digital circuitry can operate. The displays on such instruments take this into account so they still display the correct value, microwave frequency counters can currently measure frequencies up to almost 56 GHz. The accuracy of a counter is strongly dependent on the stability of its timebase. A timebase is very delicate like the hands of a watch and this can make a frequency reading, when referenced to the timebase, seem higher or lower than the actual value. For higher accuracy measurements, a frequency reference tied to a very high stability oscillator such as a GPS disciplined rubidium oscillator may be used. Where the frequency does not need to be known to such a degree of accuracy. It is also possible to measure using the same techniques in software in an embedded system
4.
Hewlett-Packard
–
The Hewlett-Packard Company or shortened to Hewlett-Packard was an American multinational information technology company headquartered in Palo Alto, California. The company was founded in a garage in Palo Alto by William Bill Redington Hewlett and David Dave Packard. HP was the worlds leading PC manufacturer from 2007 to Q22013 and it specialized in developing and manufacturing computing, data storage, and networking hardware, designing software and delivering services. HP also had services and consulting business around its products and partner products.4 billion in 2008, in November 2009, HP announced the acquisition of 3Com, with the deal closing on April 12,2010. On April 28,2010, HP announced the buyout of Palm, on September 2,2010, HP won its bidding war for 3PAR with a $33 a share offer, which Dell declined to match. On October 6,2014, Hewlett-Packard announced plans to split the PC and printers business from its enterprise products, the split closed on November 1,2015, and resulted in two publicly traded companies, HP Inc. and Hewlett Packard Enterprise. William Redington Hewlett and David Packard graduated with degrees in engineering from Stanford University in 1935. The company originated in a garage in nearby Palo Alto during a fellowship they had with a past professor, Terman was considered a mentor to them in forming Hewlett-Packard. In 1939, Packard and Hewlett established Hewlett-Packard in Packards garage with a capital investment of US$538. Hewlett and Packard tossed a coin to decide whether the company they founded would be called Hewlett-Packard or Packard-Hewlett, HP incorporated on August 18,1947, and went public on November 6,1957. Of the many projects they worked on, their very first financially successful product was an audio oscillator. This allowed them to sell the Model 200A for $54.40 when competitors were selling less stable oscillators for over $200, the Model 200 series of generators continued until at least 1972 as the 200AB, still tube-based but improved in design through the years. They worked on technology and artillery shell fuses during World War II. Hewlett-Packards HP Associates division, established around 1960, developed semiconductor devices primarily for internal use, instruments and calculators were some of the products using these devices. HP partnered in the 1960s with Sony and the Yokogawa Electric companies in Japan to develop several high-quality products, the products were not a huge success, as there were high costs in building HP-looking products in Japan. HP and Yokogawa formed a joint venture in 1963 to market HP products in Japan, HP bought Yokogawa Electrics share of Hewlett-Packard Japan in 1999. HP spun off a company, Dynac, to specialize in digital equipment. The name was picked so that the HP logo hp could be turned upside down to be a reverse image of the logo dy of the new company
5.
Calculator
–
An electronic calculator is a small, portable electronic device used to perform operations ranging from basic arithmetic to complex mathematics. The first solid state electronic calculator was created in the 1960s, building on the history of tools such as the abacus. It was developed in parallel with the computers of the day. The pocket sized devices became available in the 1970s, especially after the first microprocessor and they later became used commonly within the petroleum industry. Modern electronic calculators vary, from cheap, give-away, credit-card-sized models to sturdy desktop models with built-in printers and they became popular in the mid-1970s. By the end of decade, calculator prices had reduced to a point where a basic calculator was affordable to most. In addition to general purpose calculators, there are designed for specific markets. For example, there are scientific calculators which include trigonometric and statistical calculations, some calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, as of 2016, basic calculators cost little, but the scientific and graphing models tend to cost more. In 1986, calculators still represented an estimated 41% of the worlds general-purpose hardware capacity to compute information, by 2007, this diminished to less than 0. 05%. Modern 2016 electronic calculators contain a keyboard with buttons for digits and arithmetical operations, most basic calculators assign only one digit or operation on each button, however, in more specific calculators, a button can perform multi-function working with key combinations. Large-sized figures and comma separators are used to improve readability. Various symbols for function commands may also be shown on the display, fractions such as 1⁄3 are displayed as decimal approximations, for example rounded to 0.33333333. Also, some fractions can be difficult to recognize in decimal form, as a result, Calculators also have the ability to store numbers into computer memory. Basic types of these only one number at a time. The variables can also be used for constructing formulas, some models have the ability to extend memory capacity to store more numbers, the extended memory address is termed an array index. Power sources of calculators are, batteries, solar cells or mains electricity, some models even have no turn-off button but they provide some way to put off. Crank-powered calculators were also common in the computer era
6.
HP-25
–
The HP-25 was a hand-held programmable scientific/engineering calculator made by Hewlett-Packard between 1975 and 1978. The HP-25 was introduced as an alternative to the ground-breaking HP-65. To reduce cost, the HP-25 omitted the HP-65s magnetic card reader, after switching off, the program was lost and had to be typed in again. The model HP-25C, introduced in 1976, addressed that shortcoming through the first use of battery-backed CMOS memory in a calculator, like all early HP calculators, the 25 used the Reverse Polish Notation for entering calculations, working on a four-level stack. Nearly all buttons had two functions, accessed by a blue and yellow prefix key. A small sliding switch was used to change between run and program mode. g, the HP-25 had memory space for up to 49 program steps. It was the first HP calculator which used fully merged keycodes to save memory space, additionally there were eight storage registers and specialized scientific and statistical functions. The owners manual came with 161 pages in four colors and contained many mathematical, scientific, the HP-25 was about 25% smaller than the HP-65. It used the same trapezoid profiled keys introduced wih the HP-65, the HP-25 was regarded as a competitor to the TI-58 and TI-58C calculators offered by Texas Instruments. Looking strictly at the functionality and capacity, the more equal competitor would be the TI-57 and it lacked a few of the HP-25s functions, but had some other advantages. One notable deficiency of the HP-25/25C was the lack of a capability, at a time when the TI-58. HP would go on to introduce the HP-29C/19C calculators with 99 merged steps, labels, and TI would introduce a TI-58C with continuous memory
7.
Commodore International
–
Commodore International was a North American home computer and electronics manufacturer. Commodore International, along with its subsidiary Commodore Business Machines, participated in the development of the computer industry in the 1970s and 1980s. The company developed and marketed one of the worlds best-selling desktop computers, the company that would become Commodore Business Machines, Inc. was founded in 1954 in Toronto as the Commodore Portable Typewriter Company by Polish immigrant and Auschwitz survivor Jack Tramiel. He moved to Toronto to start production, by the late 1950s a wave of Japanese machines forced most North American typewriter companies to cease business, but Tramiel instead turned to adding machines. In 1955, the company was incorporated as Commodore Business Machines. In 1962, Commodore went public on the New York Stock Exchange, in the late 1960s, history repeated itself when Japanese firms started producing and exporting adding machines. The companys main investor and chairman, Irving Gould, suggested that Tramiel travel to Japan to understand how to compete, instead, he returned with the new idea to produce electronic calculators, which were just coming on the market. Commodore soon had a profitable calculator line and was one of the popular brands in the early 1970s. However, in 1975, Texas Instruments, the supplier of calculator parts, entered the market directly. Commodore obtained an infusion of cash from Gould, which Tramiel used beginning in 1976 to purchase several second-source chip suppliers, including MOS Technology, Inc. in order to assure his supply. He agreed to buy MOS, which was having troubles of its own, through the 1970s, Commodore also produced numerous peripherals and consumer electronic products such as the Chessmate, a chess computer based around a MOS6504 chip, released in 1978. In December 2007 when Tramiel was visiting the Computer History Museum in Mountain View, California, for the 25th anniversary of the Commodore 64 and he said, I wanted to call my company General, but theres so many Generals in the U. S. Then I went to Admiral, but that was taken, so I wind up in Berlin, Germany, with my wife, and we were in a cab, and the cab made a short stop, and in front of us was an Opel Commodore. Tramiel gave this account in interviews, but Opels Commodore didnt debut until 1967. Once Chuck Peddle had taken over engineering at Commodore, he convinced Jack Tramiel that calculators were already a dead end, from PETs 1977 debut, Commodore would be a computer company. The operational headquarters, where research and development of new products occurred, retained the name Commodore Business Machines, in 1980 Commodore launched production for the European market in Braunschweig. By 1980 Commodore was one of the three largest microcomputer companies, and the largest in the Common Market and this was addressed with the introduction of the VIC-20 in 1981, which was introduced at a cost of US$299 and sold in retail stores. Commodore took out ads featuring William Shatner asking consumers Why buy just a video game
8.
Texas Instruments
–
Texas Instruments Inc. is an American technology company that designs and manufactures semiconductors, which it sells to electronics designers and manufacturers globally. Headquartered in Dallas, Texas, United States, TI is one of the top ten semiconductor companies worldwide, Texas Instrumentss focus is on developing analog chips and embedded processors, which accounts for more than 85% of their revenue. TI also produces TI digital light processing technology and education technology products including calculators, microcontrollers, to date, TI has more than 43,000 patents worldwide. TI produced the worlds first commercial silicon transistor in 1950, Jack Kilby invented the integrated circuit in 1958 while working at TIs Central Research Labs. TI also invented the hand-held calculator in 1967, and introduced the first single-chip microcontroller in 1970, in 1987, TI invented the digital light processing device, which serves as the foundation for the companys award-winning DLP technology and DLP Cinema. In 1990, TI came out with the popular TI-81 calculator which made them a leader in the calculator industry. In 1997, its business was sold to Raytheon, which allowed TI to strengthen its focus on digital solutions. Texas Instruments was founded by Cecil H. Green, J. Erik Jonsson, Eugene McDermott, McDermott was one of the original founders of Geophysical Service Inc. in 1930. McDermott, Green, and Jonsson were GSI employees who purchased the company in 1941, in November,1945, Patrick Haggerty was hired as general manager of the Laboratory and Manufacturing division, which focused on electronic equipment. By 1951, the L&M division, with its contracts, was growing faster than GSIs Geophysical division. The company was reorganized and initially renamed General Instruments Inc, because there already existed a firm named General Instrument, the company was renamed Texas Instruments that same year. From 1956 to 1961, Fred Agnich of Dallas, later a Republican member of the Texas House of Representatives, was the Texas Instruments president, Geophysical Service, Inc. became a subsidiary of Texas Instruments. Early in 1988 most of GSI was sold to the Halliburton Company, in 1930, J. Clarence Karcher and Eugene McDermott founded Geophysical Service, an early provider of seismic exploration services to the petroleum industry. In 1939, the company reorganized as Coronado Corp. an oil company with Geophysical Service Inc, on December 6,1941, McDermott along with three other GSI employees, J. Erik Jonsson, Cecil H. Green, and H. B. During World War II, GSI expanded their services to include electronics for the U. S. Army, Signal Corps, in 1951, the company changed its name to Texas Instruments, GSI becoming a wholly owned subsidiary of the new company. Texas Instruments also continued to manufacture equipment for use in the seismic industry, after selling GSI, TI finally sold the company to Halliburton in 1988, at which point GSI ceased to exist as a separate entity. Texas Instruments entered the electronics market in 1942 with submarine detection equipment. During the early 1980s, Texas Instruments instituted a quality program which included Juran training, as well as promoting statistical process control, Taguchi methods and Design for Six Sigma
9.
TI-30
–
The TI-30 was a scientific calculator manufactured by Texas Instruments, the first model of which was introduced in 1976. While the original TI-30 left production in 1983 after several revisions, TI maintains the TI-30 designation as a branding for its low. The original TI-30 was notable for its low cost for the time. This was much less than the prices of other scientific calculators of the era, for example. The Casio FX-20, another popular scientific calculator, sold for roughly double the price of the TI-30, the TI-30 sold for less than the cost of a professional grade slide rule. The TI-30 sold an estimated 15 million units during its lifespan from 1976–1983, although the MSRP in the US was US$24.95 at introduction, it is rumored that the original TI-30 got its name from a planned retail price of US$29.95 or $30. The TI-30 could perform all the logarithmic and trigonometric functions of an HP-21. Although the Texas Instruments SR-50 pioneered algebraic notation with precedence and parentheses in 1974, early production TI-30 units contained a logic error in their calculation of inverse tangents. On these early models, pressing 0 INV TAN would cause the calculator to go into a loop until it was powered off with the OFF button. The 0 had to be pressed on the keyboard, the calculator produced a correct answer if the 0 was the result of a previous calculation, the TI-30 was at one point the most popular scientific calculator for junior high and high school use in the United States. The book alone retailed for $12.95 and many considered the book to be more valuable than the calculator itself. In 1980, Texas Instruments converted the TI-30 to use a liquid crystal display, releasing the TI-30 LCD in Europe and the TI-30 II a year later in the U. S. The calculator itself remained functionally similar over several redesigns in the few years. The earliest model, however, ran off of a 9 volt battery, the low cost, bulky case and easily accessible matrix keyboard made the TI-30 ideal for homebrew electronics projects requiring a large number of keys in a small package. Currently the bottom of the TI-30 line, the Xa has a standard one-line, the solar-powered eco RS model is available only in Europe. TI-30Xa Solar School Edition, A modified version of the TI-30Xa and this calculator is approved for Virginia State Testing. TI-30X IIS and TI-30X IIB, added a two-line, scrollable display, tI-30XS and TI-30XB MultiView, first non-graphing TI calculators with a dot-matrix display, able to display expressions in textbook-style notation. Uses a command similar to TI-BASIC, but with no programming capability
10.
Casio
–
Casio Computer Co. Ltd. is a multinational consumer electronics and commercial electronics manufacturing company headquartered in Shibuya, Tokyo, Japan. Its products include calculators, mobile phones, digital cameras, electronic musical instruments and it was founded in 1946, and in 1957 released the worlds first entirely electric compact calculator. Casio was a digital camera innovator, and during the 1980s and 1990s. Casio was established in April 1946 by Tadao Kashio, an engineer specializing in fabrication technology. Kashios first major product was the pipe, a finger ring that would hold a cigarette. Japan was impoverished immediately following World War II, so cigarettes were valuable, after seeing the electric calculators at the first Business Show in Ginza, Tokyo in 1949, Kashio and his younger brothers used their profits from the yubiwa pipe to develop their own calculators. Most of the calculators at that time worked using gears and could be operated by using a crank or using a motor. Toshio possessed some knowledge of electronics, and set out to make a calculator using solenoids, the desk-sized calculator was finished in 1954 and was Japans first electro-mechanical calculator. Another distinguishing innovation was the use of a display window instead of the three display windows used in other calculators. In 1957 Casio released the Model 14-A, sold for 485,000 yen, the worlds first all-electric compact calculator,1957 also marked the establishment of Casio Computer Co. Ltd. In the 1980s, its budget electronic instruments and its line of home electronic musical keyboard instruments became popular. The company also became known for the wide variety and innovation of its wristwatches. It was one of the earliest manufacturers of quartz watches, both digital and analog and it also began selling calculator watches during this time. In the 1970s and 80s, Casio was known for its electronic calculators, today, Casio is most commonly known for making durable and reliable digital watches. The G-Shock range of shock resistant watches is popular, with the 1983 G-Shock DW-5600C being highly sought-after by collectors, Casio made a variety of digital watches with in-built games in the 1980s and 90s, which were highly popular at the time. Casio also makes products for local markets, including a Prayer Compass watch designed to help Muslims pray on time, note, This is a list of selected calculators. Figures in parentheses imply approximate year of introduction, note, This is a list of selected models. Wiki collection of works on Casio
11.
Casio FX-502P series
–
The FX-501P and FX-502P were programmable calculators, manufactured by CASIO from 1978. They were the predecessors of the Casio FX-601P and Casio FX-602P, the FX-502P series use the algebraic logic as was state of the art at the time. The FX-501P and FX-502P featured a single line 7-segment liquid crystal display with 10 digits as main display, an additional 3 digits 7-segment display used to display exponents and program steps when entering or debugging programs and 10 status indicators. The display was covered with a filter, supposedly to prevent ultra-violet radiation damage. The programming model employed was key stroke programming by which each key pressed was recorded, on record multiple key presses were merged into a single programming step. All operations fitted into one program step, the FX-501P could store 128 steps, with 11 memory registers. The FX-502P had double capacity with 256 steps and 22 memory registers, conditional and Unconditional jumps as well as subroutines where supported. The FX-502P series supported 10 labels for programs and subroutines called P0, each program or subroutine could have up to 10 local labels called LBL0. The FX-501P and FX-502P supported indirect addressing both for access and jumps and therefore the programming model could be considered Turing complete. Since the FX-501P and FX-502P only employed a Seven-segment display each program step was represented by a special 2 digit codes made op of the digits 0,9 and the character C, E, F and P. The Calculator came with a special overlay so the user need not memorise the mapping between code and actual command, what differentiated the 501/502P from its competitors was that programming was retained in a battery-buffered memory when the calculator was turned off. Texas Instruments And Hewlett Packard had comparable devices but without the constant memory capability, here is a sample program that computes the factorial of an integer number from 2 to 69. Youll type 5 P0 and get the result,120, the whole program is only 9 bytes long. The FX-501P and FX-502P used the FA-1 to store program and data to Compact Cassette using the Kansas City standard, the FA-1 also enabled the calculators to generate musical notes. FX-501P and FX-502P on RS-Key maintained by Viktor Toth, fX502P Geek on casio. ledudu. com casio fx-501p and casio fx-502p on Voidware FX-502p Simulator
12.
Casio 9860 series
–
The Casio fx-9860G is a series of graphing calculators manufactured by Casio Computer Co. Ltd, successor of the fx-9750G PLUS/CFX-9850 PLUS/CFX-9950 PLUS/CFX-9970 family of calculators, changes from fx-9750G PLUS, CFX-9850 PLUS, CFX-9950 PLUS, CFX-9970 series include, Increase program capacity to 63000 bytes and storage memory capacity to 1. 5MB. For models with SD suffix, support of Secure Digital memory cards, there are several versions of the fx-9860G, the standard fx-9860G, often referred to as the vanilla flavor, and the SD, AU and Slim versions. The AU version used to limit the amount of flash memory available to 800 Kb to meet Australian school regulations. The SD variant comes with an SD expansion card slot, allowing read, the Slim version has a back-lit display, on-board help, and is designed as a clam-shell to minimize its size. The usual fx-9860G and fx-9860G SD are marketed in France as Graph85 and Graph85 SD, the calculators can be programmed in different ways. The fx-9860Gs come with a built-in BASIC-like interpreter, allowing the user to create simple, the other method is to create an add-in. Add-ins are binary programs, executing directly on the calculators CPU, CASIO has released two official add-ins, GEOMETRY and PHYSIUM. An SDK was released by CASIO in 22/01/2007, allowing users to create their own add-ins, the add-ins and the SDK are available for registered users at CASIOs website. The calculator supports connecting to computer via USB cable, USB connectivity requires installation of USB driver and Program Link software from the bundled CD-ROM. The 3-pin COM port supports transferring data between other CFX-9850/fx-7400 series calculator up to 9600bps, and other fx-9860G series calculator up to 115200bps, the fx-9860GII and fx-9860GII SD became available in May 2009. These calculators have backlit displays and the Geometry and ECON2 apps preinstalled and they also have new mathematical functions. The French versions of the GII models are the Graph 75, the Australian version of the GII is the fx-9860G AU PLUS. Product page Product page Product page
13.
Uncertainty
–
Uncertainty is a situation which involves imperfect and/or unknown information. However, uncertainty is an expression without a straightforward description. It applies to predictions of events, to physical measurements that are already made. Uncertainty arises in partially observable and/or stochastic environments, as well as due to ignorance and/or indolence, a state of having limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome. Risk A state of uncertainty where some possible outcomes have an effect or significant loss. Measurement of risk A set of measured uncertainties where some possible outcomes are losses, and the magnitudes of those losses – this also includes loss functions over continuous variables. It will appear that a measurable uncertainty, or risk proper, if probabilities are applied to the possible outcomes using weather forecasts or even just a calibrated probability assessment, the uncertainty has been quantified. Suppose it is quantified as a 90% chance of sunshine, if there is a major, costly, outdoor event planned for tomorrow then there is a risk since there is a 10% chance of rain, and rain would be undesirable. Furthermore, if this is an event and $100,000 would be lost if it rains. These situations can be even more realistic by quantifying light rain vs. heavy rain. Some may represent the risk in this example as the expected opportunity loss or the chance of the loss multiplied by the amount of the loss and that is useful if the organizer of the event is risk neutral, which most people are not. Most would be willing to pay a premium to avoid the loss, an insurance company, for example, would compute an EOL as a minimum for any insurance coverage, then add onto that other operating costs and profit. Since many people are willing to buy insurance for many reasons, quantitative uses of the terms uncertainty and risk are fairly consistent from fields such as probability theory, actuarial science, and information theory. Some also create new terms without substantially changing the definitions of uncertainty or risk, for example, surprisal is a variation on uncertainty sometimes used in information theory. But outside of the more mathematical uses of the term, usage may vary widely, in cognitive psychology, uncertainty can be real, or just a matter of perception, such as expectations, threats, etc. Vagueness or ambiguity are sometimes described as second order uncertainty, where there is uncertainty even about the definitions of uncertain states or outcomes, the difference here is that this uncertainty is about the human definitions and concepts, not an objective fact of nature. It is usually modelled by some variation on Zadehs fuzzy logic and it has been argued that ambiguity, however, is always avoidable while uncertainty is not necessarily avoidable. Uncertainty may be purely a consequence of a lack of knowledge of obtainable facts and that is, there may be uncertainty about whether a new rocket design will work, but this uncertainty can be removed with further analysis and experimentation
14.
Speed of light
–
The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299792458 metres per second, it is exact because the unit of length, the metre, is defined from this constant, according to special relativity, c is the maximum speed at which all matter and hence information in the universe can travel. It is the speed at which all particles and changes of the associated fields travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the reference frame of the observer. In the theory of relativity, c interrelates space and time, the speed at which light propagates through transparent materials, such as glass or air, is less than c, similarly, the speed of radio waves in wire cables is slower than c. The ratio between c and the speed v at which light travels in a material is called the index n of the material. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, the light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light limits the theoretical maximum speed of computers. The speed of light can be used time of flight measurements to measure large distances to high precision. Ole Rømer first demonstrated in 1676 that light travels at a speed by studying the apparent motion of Jupiters moon Io. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, in 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame is a constant and is independent of the motion of the light source. He explored the consequences of that postulate by deriving the theory of relativity and in doing so showed that the parameter c had relevance outside of the context of light and electromagnetism. After centuries of increasingly precise measurements, in 1975 the speed of light was known to be 299792458 m/s with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units as the distance travelled by light in vacuum in 1/299792458 of a second, as a result, the numerical value of c in metres per second is now fixed exactly by the definition of the metre. The speed of light in vacuum is usually denoted by a lowercase c, historically, the symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant later shown to equal √2 times the speed of light in vacuum, in 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum. This article uses c exclusively for the speed of light in vacuum, since 1983, the metre has been defined in the International System of Units as the distance light travels in vacuum in 1⁄299792458 of a second
15.
Orders of magnitude (numbers)
–
This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Mathematics – Writing, Approximately 10−183,800 is a rough first estimate of the probability that a monkey, however, taking punctuation, capitalization, and spacing into account, the actual probability is far lower, around 10−360,783. Computing, The number 1×10−6176 is equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value, Computing, The number 6. 5×10−4966 is approximately equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE floating-point value. Computing, The number 3. 6×10−4951 is approximately equal to the smallest positive non-zero value that can be represented by a 80-bit x86 double-extended IEEE floating-point value. Computing, The number 1×10−398 is equal to the smallest positive non-zero value that can be represented by a double-precision IEEE decimal floating-point value, Computing, The number 4. 9×10−324 is approximately equal to the smallest positive non-zero value that can be represented by a double-precision IEEE floating-point value. Computing, The number 1×10−101 is equal to the smallest positive non-zero value that can be represented by a single-precision IEEE decimal floating-point value, Mathematics, The probability in a game of bridge of all four players getting a complete suit is approximately 4. 47×10−28. ISO, yocto- ISO, zepto- Mathematics, The probability of matching 20 numbers for 20 in a game of keno is approximately 2.83 × 10−19. ISO, atto- Mathematics, The probability of rolling snake eyes 10 times in a row on a pair of dice is about 2. 74×10−16. ISO, micro- Mathematics – Poker, The odds of being dealt a flush in poker are 649,739 to 1 against. Mathematics – Poker, The odds of being dealt a flush in poker are 72,192 to 1 against. Mathematics – Poker, The odds of being dealt a four of a kind in poker are 4,164 to 1 against, for a probability of 2.4 × 10−4. ISO, milli- Mathematics – Poker, The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10−3. Mathematics – Poker, The odds of being dealt a flush in poker are 507.8 to 1 against, Mathematics – Poker, The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10−3. Physics, α =0.007297352570, the fine-structure constant, ISO, deci- Mathematics – Poker, The odds of being dealt only one pair in poker are about 5 to 2 against, for a probability of 0.42. Demography, The population of Monowi, a village in Nebraska. Mathematics, √2 ≈1.414213562373095489, the ratio of the diagonal of a square to its side length. Mathematics, φ ≈1.618033988749895848, the golden ratio Mathematics, the number system understood by most computers, human scale, There are 10 digits on a pair of human hands, and 10 toes on a pair of human feet. Mathematics, The number system used in life, the decimal system, has 10 digits,0,1,2,3,4,5,6,7,8,9
16.
1,000,000,000
–
1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001. One billion can also be written as b or bn, in scientific notation, it is written as 1 ×109. The SI prefix giga indicates 1,000,000,000 times the base unit, one billion years may be called eon in astronomy and geology. Previously in British English, the word billion referred exclusively to a million millions, however, this is no longer as common as earlier, and the word has been used to mean one thousand million for some time. The alternative term one thousand million is used in the U. K. or countries such as Spain that uses one thousand million as one million million constitutes a billion. The worded figure, as opposed to the figure is used to differentiate between one thousand million or one billion. The term milliard can also be used to refer to 1,000,000,000, whereas milliard is seldom used in English, in the South Asian numbering system, it is known as 100 crore or 1 Arab. 1000000007 – smallest prime number with 10 digits,1023456789 – smallest pandigital number in base 10. 1026753849 – smallest pandigital square that includes 0,1073741824 –2301073807359 – 14th Kynea number. 1162261467 –3191220703125 –513 1232922769- 35113^2 Centered hexagonal number,1234567890 – pandigital number with the digits in order. 1882341361 – The least prime whose reversal is both square and triangular,1977326743 –7112147483647 – 8th Mersenne prime and the largest signed 32-bit integer. 2147483648 –2312176782336 –6122214502422 – 6th primary pseudoperfect number,2357947691 –1192971215073 – 11th Fibonacci prime. 3405691582 – hexadecimal CAFEBABE, used as a placeholder in programming,3405697037 – hexadecimal CAFED00D, used as a placeholder in programming. 3735928559 – hexadecimal DEADBEEF, used as a placeholder in programming,3486784401 –3204294836223 – 16th Carol number. 4294967291 – Largest prime 32-bit unsigned integer,4294967295 – Maximum 32-bit unsigned integer, perfect totient number, product of the five prime Fermat numbers. 4294967296 –2324294967297 – the first composite Fermat number,6103515625 –5146210001000 – only self-descriptive number in base 10. 6975757441 –1786983776800 – 15th colossally abundant number, 15th superior highly composite number 7645370045 – 27th Pell number,8589934592 –2339043402501 – 25th Motzkin number. 9814072356 – largest square pandigital number, largest pandigital pure power,9876543210 – largest number without redundant digits
17.
1,000,000
–
One million or one thousand thousand is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione, from mille, thousand and it is commonly abbreviated as m or M, further MM, mm, or mn in financial contexts. In scientific notation, it is written as 1×106 or 106, physical quantities can also be expressed using the SI prefix mega, when dealing with SI units, for example,1 megawatt equals 1,000,000 watts. The meaning of the word million is common to the scale and long scale numbering systems, unlike the larger numbers. Information, Not counting spaces, the text printed on 136 pages of an Encyclopædia Britannica, length, There are one million millimeters in a kilometer, and roughly a million sixteenths of an inch in a mile. A typical car tire might rotate a million times in a 1, 200-mile trip, fingers, If the width of a human finger is 2.2 cm, then a million fingers lined up would cover a distance of 22 km. If a person walks at a speed of 4 km/h, it would take approximately five. A city lot 70 by 100 feet is about a million square inches, volume, The cube root of one million is only one hundred, so a million objects or cubic units is contained in a cube only a hundred objects or linear units on a side. A million grains of salt or granulated sugar occupies only about 64 ml. One million cubic inches would be the volume of a room only 8 1⁄3 feet long by 8 1⁄3 feet wide by 8 1⁄3 feet high. Mass, A million cubic millimeters of water would have a volume of one litre, a million millilitres or cubic centimetres of water has a mass of a million grams or one tonne. Weight, A million 80-milligram honey bees would weigh the same as an 80 kg person, landscape, A pyramidal hill 600 feet wide at the base and 100 feet high would weigh about a million tons. Computer, A display resolution of 1,280 by 800 pixels contains 1,024,000 pixels, money, A USD bill of any denomination weighs 1 gram. There are 454 grams in a pound, one million $1 bills would weigh 2,204.62 pounds, or just over 1 ton. Time, A million seconds is 11.57 days, in Indian English and Pakistani English, it is also expressed as 10 lakh or 10 Lac. Lakh is derived from laksh for 100,000 in Sanskrit
18.
1 (number)
–
1, is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement, for example, a line segment of unit length is a line segment of length 1. It is also the first of the series of natural numbers. The word one can be used as a noun, an adjective and it comes from the English word an, which comes from the Proto-Germanic root *ainaz. The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no-, compare the Proto-Germanic root *ainaz to Old Frisian an, Gothic ains, Danish een, Dutch een, German eins and Old Norse einn. Compare the Proto-Indo-European root *oi-no- to Greek oinos, Latin unus, Old Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin, One, sometimes referred to as unity, is the first non-zero natural number. It is thus the integer before two and after zero, and the first positive odd number, any number multiplied by one is that number, as one is the identity for multiplication. As a result,1 is its own factorial, its own square, its own cube, One is also the result of the empty product, as any number multiplied by one is itself. It is also the natural number that is neither composite nor prime with respect to division. The Gupta wrote it as a line, and the Nagari sometimes added a small circle on the left. The Nepali also rotated it to the right but kept the circle small and this eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. Where the 1 is written with an upstroke, the number 7 has a horizontal stroke through the vertical line. While the shape of the 1 character has an ascender in most modern typefaces, in typefaces with text figures, many older typewriters do not have a separate symbol for 1 and use the lowercase letter l instead. It is possible to find cases when the uppercase J is used,1 cannot be used as the base of a positional numeral system, as the only digit that would be permitted in such a system would be 0. Since the base 1 exponential function always equals 1, its inverse does not exist, there are two ways to write the real number 1 as a recurring decimal, as 1.000. and as 0.999. There is only one way to represent the real number 1 as a Dedekind cut, in a multiplicative group or monoid, the identity element is sometimes denoted 1, but e is also traditional. However,1 is especially common for the identity of a ring. When such a ring has characteristic n not equal to 0,1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few
19.
Binary number
–
The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
20.
Floating-point arithmetic
–
In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision. A number is, in general, represented approximately to a number of significant digits and scaled using an exponent in some fixed base. For example,1.2345 =12345 ⏟ significand ×10 ⏟ base −4 ⏞ exponent, the term floating point refers to the fact that a numbers radix point can float, that is, it can be placed anywhere relative to the significant digits of the number. This position is indicated as the exponent component, and thus the floating-point representation can be thought of as a kind of scientific notation. The result of dynamic range is that the numbers that can be represented are not uniformly spaced. Over the years, a variety of floating-point representations have been used in computers, however, since the 1990s, the most commonly encountered representation is that defined by the IEEE754 Standard. A floating-point unit is a part of a computer system designed to carry out operations on floating point numbers. A number representation specifies some way of encoding a number, usually as a string of digits, there are several mechanisms by which strings of digits can represent numbers. In common mathematical notation, the string can be of any length. If the radix point is not specified, then the string implicitly represents an integer, in fixed-point systems, a position in the string is specified for the radix point. So a fixed-point scheme might be to use a string of 8 decimal digits with the point in the middle. The scaling factor, as a power of ten, is then indicated separately at the end of the number, floating-point representation is similar in concept to scientific notation. Logically, a floating-point number consists of, A signed digit string of a length in a given base. This digit string is referred to as the significand, mantissa, the length of the significand determines the precision to which numbers can be represented. The radix point position is assumed always to be somewhere within the significand—often just after or just before the most significant digit and this article generally follows the convention that the radix point is set just after the most significant digit. A signed integer exponent, which modifies the magnitude of the number, using base-10 as an example, the number 7005152853504700000♠152853.5047, which has ten decimal digits of precision, is represented as the significand 1528535047 together with 5 as the exponent. In storing such a number, the base need not be stored, since it will be the same for the range of supported numbers. Symbolically, this value is, s b p −1 × b e, where s is the significand, p is the precision, b is the base
21.
Binary prefix
–
A binary prefix is a unit prefix for multiples of units in data processing, data transmission, and digital information, notably the bit and the byte, to indicate multiplication by a power of 2. The computer industry has used the units kilobyte, megabyte, and gigabyte, and the corresponding symbols KB, MB. In citations of main memory capacity, gigabyte customarily means 1073741824 bytes, as this is the third power of 1024, and 1024 is a power of two, this usage is referred to as a binary measurement. In most other contexts, the uses the multipliers kilo, mega, giga, etc. in a manner consistent with their meaning in the International System of Units. For example, a 500 gigabyte hard disk holds 500000000000 bytes, in contrast with the binary prefix usage, this use is described as a decimal prefix, as 1000 is a power of 10. The use of the same unit prefixes with two different meanings has caused confusion, in 2008, the IEC prefixes were incorporated into the ISO/IEC80000 standard. Early computers used one of two addressing methods to access the memory, binary or decimal. For example, the IBM701 used binary and could address 2048 words of 36 bits each, while the IBM702 used decimal, by the mid-1960s, binary addressing had become the standard architecture in most computer designs, and main memory sizes were most commonly powers of two. Early computer system documentation would specify the size with an exact number such as 4096,8192. These are all powers of two, and furthermore are small multiples of 210, or 1024, as storage capacities increased, several different methods were developed to abbreviate these quantities. The method most commonly used today uses prefixes such as kilo, mega, giga, and corresponding symbols K, M, and G, the prefixes kilo- and mega-, meaning 1000 and 1000000 respectively, were commonly used in the electronics industry before World War II. Along with giga- or G-, meaning 1000000000, they are now known as SI prefixes after the International System of Units, introduced in 1960 to formalize aspects of the metric system. The International System of Units does not define units for digital information and this usage is not consistent with the SI. Compliance with the SI requires that the prefixes take their 1000-based meaning, the use of K in the binary sense as in a 32K core meaning 32 ×1024 words, i. e.32768 words, can be found as early as 1959. Gene Amdahls seminal 1964 article on IBM System/360 used 1K to mean 1024 and this style was used by other computer vendors, the CDC7600 System Description made extensive use of K as 1024. Thus the first binary prefix was born, the exact values 32768 words,65536 words and 131072 words would then be described as 32K, 65K and 131K. This style was used from about 1965 to 1975 and these two styles were used loosely around the same time, sometimes by the same company. In discussions of binary-addressed memories, the size was evident from context
22.
IEC prefix
–
A binary prefix is a unit prefix for multiples of units in data processing, data transmission, and digital information, notably the bit and the byte, to indicate multiplication by a power of 2. The computer industry has used the units kilobyte, megabyte, and gigabyte, and the corresponding symbols KB, MB. In citations of main memory capacity, gigabyte customarily means 1073741824 bytes, as this is the third power of 1024, and 1024 is a power of two, this usage is referred to as a binary measurement. In most other contexts, the uses the multipliers kilo, mega, giga, etc. in a manner consistent with their meaning in the International System of Units. For example, a 500 gigabyte hard disk holds 500000000000 bytes, in contrast with the binary prefix usage, this use is described as a decimal prefix, as 1000 is a power of 10. The use of the same unit prefixes with two different meanings has caused confusion, in 2008, the IEC prefixes were incorporated into the ISO/IEC80000 standard. Early computers used one of two addressing methods to access the memory, binary or decimal. For example, the IBM701 used binary and could address 2048 words of 36 bits each, while the IBM702 used decimal, by the mid-1960s, binary addressing had become the standard architecture in most computer designs, and main memory sizes were most commonly powers of two. Early computer system documentation would specify the size with an exact number such as 4096,8192. These are all powers of two, and furthermore are small multiples of 210, or 1024, as storage capacities increased, several different methods were developed to abbreviate these quantities. The method most commonly used today uses prefixes such as kilo, mega, giga, and corresponding symbols K, M, and G, the prefixes kilo- and mega-, meaning 1000 and 1000000 respectively, were commonly used in the electronics industry before World War II. Along with giga- or G-, meaning 1000000000, they are now known as SI prefixes after the International System of Units, introduced in 1960 to formalize aspects of the metric system. The International System of Units does not define units for digital information and this usage is not consistent with the SI. Compliance with the SI requires that the prefixes take their 1000-based meaning, the use of K in the binary sense as in a 32K core meaning 32 ×1024 words, i. e.32768 words, can be found as early as 1959. Gene Amdahls seminal 1964 article on IBM System/360 used 1K to mean 1024 and this style was used by other computer vendors, the CDC7600 System Description made extensive use of K as 1024. Thus the first binary prefix was born, the exact values 32768 words,65536 words and 131072 words would then be described as 32K, 65K and 131K. This style was used from about 1965 to 1975 and these two styles were used loosely around the same time, sometimes by the same company. In discussions of binary-addressed memories, the size was evident from context
23.
Power of two
–
In mathematics, a power of two means a number of the form 2n where n is an integer, i. e. the result of exponentiation with number two as the base and integer n as the exponent. In a context where only integers are considered, n is restricted to values, so we have 1,2. Because two is the base of the numeral system, powers of two are common in computer science. Written in binary, a power of two always has the form 100…000 or 0. 00…001, just like a power of ten in the decimal system, a word, interpreted as an unsigned integer, can represent values from 0 to 2n −1 inclusively. Corresponding signed integer values can be positive, negative and zero, either way, one less than a power of two is often the upper bound of an integer in binary computers. As a consequence, numbers of this show up frequently in computer software. For example, in the original Legend of Zelda the main character was limited to carrying 255 rupees at any time. Powers of two are used to measure computer memory. A byte is now considered eight bits (an octet, resulting in the possibility of 256 values, the prefix kilo, in conjunction with byte, may be, and has traditionally been, used, to mean 1,024. However, in general, the term kilo has been used in the International System of Units to mean 1,000, binary prefixes have been standardized, such as kibi meaning 1,024. Nearly all processor registers have sizes that are powers of two,32 or 64 being most common, powers of two occur in a range of other places as well. For many disk drives, at least one of the size, number of sectors per track. The logical block size is almost always a power of two. Numbers that are not powers of two occur in a number of situations, such as video resolutions, but they are often the sum or product of two or three powers of two, or powers of two minus one. For example,640 =512 +128 =128 ×5, put another way, they have fairly regular bit patterns. A prime number that is one less than a power of two is called a Mersenne prime, for example, the prime number 31 is a Mersenne prime because it is 1 less than 32. Similarly, a number that is one more than a positive power of two is called a Fermat prime—the exponent itself is a power of two. A fraction that has a power of two as its denominator is called a dyadic rational, the numbers that can be represented as sums of consecutive positive integers are called polite numbers, they are exactly the numbers that are not powers of two
24.
International System of Units
–
The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
25.
NIST
–
The National Institute of Standards and Technology is a measurement standards laboratory, and a non-regulatory agency of the United States Department of Commerce. Its mission is to promote innovation and industrial competitiveness, in 1821, John Quincy Adams had declared Weights and measures may be ranked among the necessities of life to every individual of human society. From 1830 until 1901, the role of overseeing weights and measures was carried out by the Office of Standard Weights and Measures, president Theodore Roosevelt appointed Samuel W. Stratton as the first director. The budget for the first year of operation was $40,000, a laboratory site was constructed in Washington, DC, and instruments were acquired from the national physical laboratories of Europe. In addition to weights and measures, the Bureau developed instruments for electrical units, in 1905 a meeting was called that would be the first National Conference on Weights and Measures. Quality standards were developed for products including some types of clothing, automobile brake systems and headlamps, antifreeze, during World War I, the Bureau worked on multiple problems related to war production, even operating its own facility to produce optical glass when European supplies were cut off. Between the wars, Harry Diamond of the Bureau developed a blind approach radio aircraft landing system, in 1948, financed by the Air Force, the Bureau began design and construction of SEAC, the Standards Eastern Automatic Computer. The computer went into operation in May 1950 using a combination of vacuum tubes, about the same time the Standards Western Automatic Computer, was built at the Los Angeles office of the NBS and used for research there. A mobile version, DYSEAC, was built for the Signal Corps in 1954, due to a changing mission, the National Bureau of Standards became the National Institute of Standards and Technology in 1988. Following 9/11, NIST conducted the investigation into the collapse of the World Trade Center buildings. NIST had a budget for fiscal year 2007 of about $843.3 million. NISTs 2009 budget was $992 million, and it also received $610 million as part of the American Recovery, NIST employs about 2,900 scientists, engineers, technicians, and support and administrative personnel. About 1,800 NIST associates complement the staff, in addition, NIST partners with 1,400 manufacturing specialists and staff at nearly 350 affiliated centers around the country. NIST publishes the Handbook 44 that provides the Specifications, tolerances, the Congress of 1866 made use of the metric system in commerce a legally protected activity through the passage of Metric Act of 1866. NIST is headquartered in Gaithersburg, Maryland, and operates a facility in Boulder, nISTs activities are organized into laboratory programs and extramural programs. Effective October 1,2010, NIST was realigned by reducing the number of NIST laboratory units from ten to six, nISTs Boulder laboratories are best known for NIST‑F1, which houses an atomic clock. NIST‑F1 serves as the source of the official time. NIST also operates a neutron science user facility, the NIST Center for Neutron Research, the NCNR provides scientists access to a variety of neutron scattering instruments, which they use in many research fields