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54-464: The numerical prefix ' tri- ' yes (Tri being three) in Trionic. 'Ion' comes from the fact that it uses ion current, measured by the spark plugs between combustion events which acts as a sensor for knock, misfire and synchronization detection. The ion current stream which was developed within the ion sensing system due to combustion can be deduced by monitoring the secondary current of the ignition coil. Using

108-404: A desired range, between 1 and 10 for normalized notation. If the decimal was moved to the left, append × 10 ; to the right, × 10 . To represent the number 1,230,400 in normalized scientific notation, the decimal separator would be moved 6 digits to the left and × 10 appended, resulting in 1.2304 × 10 . The number −0.004 0321 would have its decimal separator shifted 3 digits to

162-406: A marginal position. There is also an international set of metric prefixes , which are used in the world's standard measurement system . In the following prefixes, a final vowel is normally dropped before a root that begins with a vowel, with the exceptions of bi-, which is extended to bis- before a vowel; among the other monosyllables , du- , di- , dvi- , and tri- , never vary. Words in

216-618: A multiple of 10 rather than multiplication by it. Several common-use numerical prefixes denote vulgar fractions . Words containing non-technical numerical prefixes are usually not hyphenated. This is not an absolute rule, however, and there are exceptions (for example: quarter-deck occurs in addition to quarterdeck ). There are no exceptions for words comprising technical numerical prefixes, though. Systematic names and words comprising SI prefixes and binary prefixes are not hyphenated, by definition. Nonetheless, for clarity, dictionaries list numerical prefixes in hyphenated form, to distinguish

270-399: A numerical prefix need not be related to the root language of the word that it prefixes. Some words comprising numerical prefixes are hybrid words . In certain classes of systematic names, there are a few other exceptions to the rule of using Greek-derived numerical prefixes. The IUPAC nomenclature of organic chemistry , for example, uses the numerical prefixes derived from Greek, except for

324-403: A power-of-ten system nomenclature where the exponent would be circled, e.g. 6.022 × 10 would be written as "6.022③". In normalized scientific notation, in E notation, and in engineering notation, the space (which in typesetting may be represented by a normal width space or a thin space ) that is allowed only before and after "×" or in front of "E" is sometimes omitted, though it

378-409: Is a digit in a number that adds to its precision. This includes all nonzero numbers, zeroes between significant digits, and zeroes indicated to be significant . Leading and trailing zeroes are not significant digits, because they exist only to show the scale of the number. Unfortunately, this leads to ambiguity. The number 1 230 400 is usually read to have five significant figures: 1, 2, 3, 0, and 4,

432-401: Is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal ). The integer n is called the exponent and the real number m is called the significand or mantissa . The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the fractional part of the common logarithm . If

486-470: Is added to (or subtracted from) the exponent, as shown below. Given two numbers in scientific notation, x 0 = m 0 × 10 n 0 {\displaystyle x_{0}=m_{0}\times 10^{n_{0}}} and x 1 = m 1 × 10 n 1 {\displaystyle x_{1}=m_{1}\times 10^{n_{1}}} Multiplication and division are performed using

540-703: Is discouraged for published documents by some style guides. Most popular programming languages – including Fortran , C / C++ , Python , and JavaScript – use this "E" notation, which comes from Fortran and was present in the first version released for the IBM 704 in 1956. The E notation was already used by the developers of SHARE Operating System (SOS) for the IBM 709 in 1958. Later versions of Fortran (at least since FORTRAN IV as of 1961) also use "D" to signify double precision numbers in scientific notation, and newer Fortran compilers use "Q" to signify quadruple precision . The MATLAB programming language supports

594-598: Is in turn from pro- and the Greek word for fat), and butane (from butyl , which is in turn from butyric , which is in turn from the Latin word for butter). Scientific notation Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form , since to do so would require writing out an inconveniently long string of digits. It may be referred to as scientific form or standard index form , or standard form in

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648-407: Is less common to do so before the alphabetical character. Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation. None of these alter the actual number, only how it's expressed. First, move the decimal separator point sufficient places, n , to put the number's value within

702-442: Is normally used for scientific notation, powers of other bases can be used too, base 2 being the next most commonly used one. For example, in base-2 scientific notation, the number 1001 b in binary (=9 d ) is written as 1.001 b × 2 d or 1.001 b × 10 b using binary numbers (or shorter 1.001 × 10 if binary context is obvious). In E notation, this is written as 1.001 b E11 b (or shorter: 1.001E11) with

756-465: Is rarely called scientific notation. Engineering notation allows the numbers to explicitly match their corresponding SI prefixes , which facilitates reading and oral communication. For example, 12.5 × 10  m can be read as "twelve-point-five nanometres" and written as 12.5 nm , while its scientific notation equivalent 1.25 × 10  m would likely be read out as "one-point-two-five times ten-to-the-negative-eight metres". A significant figure

810-520: Is using a letter "P" (or "p", for "power"). In this notation the significand is always meant to be hexadecimal, whereas the exponent is always meant to be decimal. This notation can be produced by implementations of the printf family of functions following the C99 specification and ( Single Unix Specification ) IEEE Std 1003.1 POSIX standard, when using the %a or %A conversion specifiers. Starting with C++11 , C++ I/O functions could parse and print

864-564: The ALGOL 68 programming language provided a choice of characters: E , e , \ , ⊥ , or 10 . The ALGOL " 10 " character was included in the Soviet GOST 10859 text encoding (1964), and was added to Unicode 5.2 (2009) as U+23E8 ⏨ DECIMAL EXPONENT SYMBOL . Some programming languages use other symbols. For instance, Simula uses & (or && for long ), as in 6.022&23 . Mathematica supports

918-573: The HP-25 ), or a pair of smaller and slightly raised digits were reserved for the exponent (e.g. 6.022 , as seen in the Commodore PR100 ). In 1976, Hewlett-Packard calculator user Jim Davidson coined the term decapower for the scientific-notation exponent to distinguish it from "normal" exponents, and suggested the letter "D" as a separator between significand and exponent in typewritten numbers (for example, 6.022D23 ); these gained some currency in

972-701: The cardinal catgegory are cardinal numbers , such as the English one , two , three , which name the count of items in a sequence. The multiple category are adverbial numbers, like the English once , twice , thrice , that specify the number of events or instances of otherwise identical or similar items. Enumeration with the distributive catgegory originally was meant to specify one each , two each or one by one , two by two , etc., giving how many items of each type are desired or had been found, although distinct word forms for that meaning are now mostly lost. The ordinal catgegory are based on ordinal numbers such as

1026-460: The "mantissa" from the decapower for typewritten numbers, as Jim also suggests. For example, 123 [ sic ] which is displayed in scientific notation as 1.23 -43 will now be written 1.23D-43 . Perhaps, as this notation gets more and more usage, the calculator manufacturers will change their keyboard abbreviations. HP's EEX and TI's EE could be changed to ED (for enter decapower). [1] "Decapower" . 52-Notes – Newsletter of

1080-442: The English first , second , third , which specify position of items in a sequence. In Latin and Greek, the ordinal forms are also used for fractions for amounts higher than 2; only the fraction ⁠ 1  / 2 ⁠ has special forms. The same suffix may be used with more than one category of number, as for example the orginary numbers second ary and terti ary and the distributive numbers bi nary and ter nary . For

1134-678: The IBM 704 EDPM: Programmer's Reference Manual (PDF) . New York: Applied Science Division and Programming Research Department, International Business Machines Corporation . pp. 9, 27 . Retrieved 2022-07-04 . (2+51+1 pages) "6. Extensions: 6.1 Extensions implemented in GNU Fortran: 6.1.8 Q exponent-letter". The GNU Fortran Compiler . 2014-06-12 . Retrieved 2022-12-21 . "The Unicode Standard" (v. 7.0.0 ed.) . Retrieved 2018-03-23 . Vanderburgh, Richard C., ed. (November 1976). "Decapower" (PDF) . 52-Notes – Newsletter of

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1188-478: The P notation as well. Meanwhile, the notation has been fully adopted by the language standard since C++17 . Apple 's Swift supports it as well. It is also required by the IEEE 754-2008 binary floating-point standard. Example: 1.3DEp42 represents 1.3DE h × 2 . Engineering notation can be viewed as a base-1000 scientific notation. Sayre, David , ed. (1956-10-15). The FORTRAN Automatic Coding System for

1242-530: The SR-52 Users Club . 1 (6). Dayton, OH: 1. V1N6P1 . Retrieved 2017-05-28 . Decapower – In the January 1976 issue of 65-Notes (V3N1p4) Jim Davidson ( HP-65 Users Club member #547) suggested the term "decapower" as a descriptor for the power-of-ten multiplier used in scientific notation displays. I'm going to begin using it in place of " exponent " which is technically incorrect, and the letter D to separate

1296-512: The SR-52 Users Club . Vol. 1, no. 6. Dayton, OH. November 1976. p. 1 . Retrieved 2018-05-07 . (NB. The term decapower was frequently used in subsequent issues of this newsletter up to at least 1978.) 電言板6 PC-U6000 PROGRAM LIBRARY [ Telephone board 6 PC-U6000 program library ] (in Japanese). Vol. 6. University Co-op. 1993. "TI-83 Programmer's Guide" (PDF) . Retrieved 2010-03-09 . "INTOUCH 4GL

1350-814: The T7 models which had a black ignition module. The ignition module on both T5 and T7 are an integral ignition coil and electronics that plug directly onto the spark plugs without the use of spark plug wires that were typically used in most engines at the time. SAAB Models Utilizing Trionic Engine Management System: Sources include: Engine management system SAAB Trionic T5.5 Numerical prefix Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers . In English and many other languages, they are used to coin numerous series of words. For example: In many European languages there are two principal systems, taken from Latin and Greek , each with several subsystems; in addition, Sanskrit occupies

1404-495: The United Kingdom), the exponent n is chosen so that the absolute value of m remains at least one but less than ten ( 1 ≤ | m | < 10 ). Thus 350 is written as 3.5 × 10 . This form allows easy comparison of numbers: numbers with bigger exponents are (due to the normalization) larger than those with smaller exponents, and subtraction of exponents gives an estimate of the number of orders of magnitude separating

1458-467: The United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations . On scientific calculators , it is usually known as "SCI" display mode. In scientific notation, nonzero numbers are written in the form or m times ten raised to the power of n , where n is an integer , and the coefficient m

1512-553: The common inheritance of Greek and Latin roots across the Romance languages , the import of much of that derived vocabulary into non-Romance languages (such as into English via Norman French ), and the borrowing of 19th and 20th century coinages into many languages, the same numerical prefixes occur in many languages. Numerical prefixes are not restricted to denoting integers. Some of the SI prefixes denote negative powers of 10, i.e. division by

1566-411: The extra digit, which may be considered a significant digit because it conveys some information leading to greater precision in measurements and in aggregations of measurements (adding them or multiplying them together). Additional information about precision can be conveyed through additional notation. It is often useful to know how exact the final digit or digits are. For instance, the accepted value of

1620-505: The final two zeroes serving only as placeholders and adding no precision. The same number, however, would be used if the last two digits were also measured precisely and found to equal 0 – seven significant figures. 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 placeholding zeroes are no longer required. Thus 1 230 400 would become 1.2304 × 10 if it had five significant digits. If

1674-500: The hundreds, there are competing forms: Those in -gent- , from the original Latin, and those in -cent- , derived from centi- , etc. plus the prefixes for 1 through 9 . Many of the items in the following tables are not in general use, but may rather be regarded as coinages by individuals. In scientific contexts, either scientific notation or SI prefixes are used to express very large or very small numbers, and not unwieldy prefixes. ( but hybrid hexadecimal ) Because of

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1728-417: The left and be −0.004 0321 . Conversion between different scientific notation representations of the same number with different exponential values is achieved by performing opposite operations of multiplication or division by a power of ten on the significand and an subtraction or addition of one on the exponent part. The decimal separator in the significand is shifted x places to the left (or right) and x

1782-413: The letter "E" now standing for "times two (10 b ) to the power" here. In order to better distinguish this base-2 exponent from a base-10 exponent, a base-2 exponent is sometimes also indicated by using the letter "B" instead of "E", a shorthand notation originally proposed by Bruce Alan Martin of Brookhaven National Laboratory in 1968, as in 1.001 b B11 b (or shorter: 1.001B11). For comparison,

1836-445: The letter "E" or "e" (for "exponent") is often used to represent "times ten raised to the power of", so that the notation m  E  n for a decimal significand m and integer exponent n means the same as m × 10 . For example 6.022 × 10 is written as 6.022E23 or 6.022e23 , and 1.6 × 10 is written as 1.6E-35 or 1.6e-35 . While common in computer output, this abbreviated version of scientific notation

1890-455: The manifold absolute pressure (MAP) sensor and the intake air charge temperature sensor to calculate the fuel injection curves, while the Trionic 7 and 8 systems are mass air flow type. Both systems have substantial differences that prevent utilization of components between the two. Generally speaking, engine tuners prefer the easier to work with Trionic 5 systems over the Trionic 7 and 8 which are more restrictive in what can be manipulated within

1944-601: The mass of the proton can properly be expressed as 1.672 621 923 69 (51) × 10  kg , which is shorthand for (1.672 621 923 69 ± 0.000 000 000 51 ) × 10  kg . However it is still unclear whether the error ( 5.1 × 10 in this case) is the maximum possible error, standard error , or some other confidence interval . Calculators and computer programs typically present very large or small numbers using scientific notation, and some can be configured to uniformly present all numbers that way. Because superscript exponents like 10 can be inconvenient to display or type,

1998-481: The name "Trionic" was not changed accordingly as it was determined that the name had value. The SAAB Trionic engine management system was developed for the 9000 and 'New Generation' 900 turbocharged engines. The engine management system was first utilized on the Saab B204 and B234 "H" engines to monitor and control the fuel injection system and turbocharging pressure control. The Trionic 5.2 and 5.5 systems utilized

2052-545: The number is negative then a minus sign precedes m , as in ordinary decimal notation. In normalized notation , the exponent is chosen so that the absolute value (modulus) of the significand m is at least 1 but less than 10. Decimal floating point is a computer arithmetic system closely related to scientific notation. Any real number can be written in the form m × 10 ^ in many ways: for example, 350 can be written as 3.5 × 10 or 35 × 10 or 350 × 10 . In normalized scientific notation (called "standard form" in

2106-512: The number were known to six or seven significant figures, it would be shown as 1.230 40 × 10 or 1.230 400 × 10 . Thus, an additional advantage of scientific notation is that the number of significant figures is unambiguous. It is customary in scientific measurement to record all the definitely known digits from the measurement and to estimate at least one additional digit if there is any information at all available on its value. The resulting number contains more information than it would without

2160-861: The numbers to be represented using the same exponential part, so that the significand can be simply added or subtracted: Next, add or subtract the significands: x 0 ± x 1 = ( m 0 ± m 1 ) × 10 n 0 {\displaystyle x_{0}\pm x_{1}=(m_{0}\pm m_{1})\times 10^{n_{0}}} An example: 2.34 × 10 − 5 + 5.67 × 10 − 6 = 2.34 × 10 − 5 + 0.567 × 10 − 5 = 2.907 × 10 − 5 {\displaystyle 2.34\times 10^{-5}+5.67\times 10^{-6}=2.34\times 10^{-5}+0.567\times 10^{-5}=2.907\times 10^{-5}} While base ten

2214-404: The numbers. It is also the form that is required when using tables of common logarithms . In normalized notation, the exponent n is negative for a number with absolute value between 0 and 1 (e.g. 0.5 is written as 5 × 10 ). The 10 and exponent are often omitted when the exponent is 0. For a series of numbers that are to be added or subtracted (or otherwise compared), it can be convenient to use

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2268-516: The prefix for 9 (as mentioned) and the prefixes from 1 to 4 (meth-, eth-, prop-, and but-), which are not derived from words for numbers. These prefixes were invented by the IUPAC, deriving them from the pre-existing names for several compounds that it was intended to preserve in the new system: methane (via methyl , which is in turn from the Greek word for wine), ethane (from ethyl coined by Justus von Liebig in 1834), propane (from propionic , which

2322-405: The prefixes from words with the same spellings (such as duo- and duo ). Several technical numerical prefixes are not derived from words for numbers. ( mega- is not derived from a number word, for example.) Similarly, some are only derived from words for numbers inasmuch as they are word play . ( Peta- is word play on penta- , for example. See its etymology for details.) The root language of

2376-453: The programmable calculator user community. The letters "E" or "D" were used as a scientific-notation separator by Sharp pocket computers released between 1987 and 1995, "E" used for 10-digit numbers and "D" used for 20-digit double-precision numbers. The Texas Instruments TI-83 and TI-84 series of calculators (1996–present) use a small capital E for the separator. In 1962, Ronald O. Whitaker of Rowco Engineering Co. proposed

2430-448: The range 1 to 10 (as in engineering notation for instance) and to bases other than 10 (for example, 3.15 × 2 ^ ). Engineering notation (often named "ENG" on scientific calculators) 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

2484-459: The right instead of the left and yield −4.0321 × 10 as a result. Converting a number from scientific notation to decimal notation, first remove the × 10 on the end, then shift the decimal separator n digits to the right (positive n ) or left (negative n ). The number 1.2304 × 10 would have its decimal separator shifted 6 digits to the right and become 1,230,400 , while −4.0321 × 10 would have its decimal separator moved 3 digits to

2538-1512: The rules for operation with exponentiation : x 0 x 1 = m 0 m 1 × 10 n 0 + n 1 {\displaystyle x_{0}x_{1}=m_{0}m_{1}\times 10^{n_{0}+n_{1}}} and x 0 x 1 = m 0 m 1 × 10 n 0 − n 1 {\displaystyle {\frac {x_{0}}{x_{1}}}={\frac {m_{0}}{m_{1}}}\times 10^{n_{0}-n_{1}}} Some examples are: 5.67 × 10 − 5 × 2.34 × 10 2 ≈ 13.3 × 10 − 5 + 2 = 13.3 × 10 − 3 = 1.33 × 10 − 2 {\displaystyle 5.67\times 10^{-5}\times 2.34\times 10^{2}\approx 13.3\times 10^{-5+2}=13.3\times 10^{-3}=1.33\times 10^{-2}} and 2.34 × 10 2 5.67 × 10 − 5 ≈ 0.413 × 10 2 − ( − 5 ) = 0.413 × 10 7 = 4.13 × 10 6 {\displaystyle {\frac {2.34\times 10^{2}}{5.67\times 10^{-5}}}\approx 0.413\times 10^{2-(-5)}=0.413\times 10^{7}=4.13\times 10^{6}} Addition and subtraction require

2592-468: The same number in decimal representation : 1.125 × 2 (using decimal representation), or 1.125B3 (still using decimal representation). Some calculators use a mixed representation for binary floating point numbers, where the exponent is displayed as decimal number even in binary mode, so the above becomes 1.001 b × 10 b or shorter 1.001B3. This is closely related to the base-2 floating-point representation commonly used in computer arithmetic, and

2646-410: The same value of m for all elements of the series. Normalized scientific form is the typical form of expression of large numbers in many fields, unless an unnormalized or differently normalized form, such as engineering notation , is desired. Normalized scientific notation is often called exponential notation – although the latter term is more general and also applies when m is not restricted to

2700-496: The shorthand notation 6.022*^23 (reserving the letter E for the mathematical constant e ). The first pocket calculators supporting scientific notation appeared in 1972. To enter numbers in scientific notation calculators include a button labeled "EXP" or "×10 ", among other variants. The displays of pocket calculators of the 1970s did not display an explicit symbol between significand and exponent; instead, one or more digits were left blank (e.g. 6.022 23 , as seen in

2754-513: The software. The intellectual rights to the Trionic 5 and 7 systems were sold in 2009 to BAIC , along with the Saab H Engine that it was designed for, as part of Saab's restructuring and transfer of ownership of General Motors to Spyker . optional on 00-02 four cylinder models Trionic systems are shortened to indicate their version; for e.g. T5, T7, T8, etc. The engines with T5 had red direct ignition modules which differentiated them visually from

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2808-456: The usage of IEC binary prefixes (e.g. 1B10 for 1×2 ( kibi ), 1B20 for 1×2 ( mebi ), 1B30 for 1×2 ( gibi ), 1B40 for 1×2 ( tebi )). Similar to "B" (or "b" ), the letters "H" (or "h" ) and "O" (or "o", or "C" ) are sometimes also used to indicate times 16 or 8 to the power as in 1.25 = 1.40 h × 10 h = 1.40H0 = 1.40h0, or 98000 = 2.7732 o × 10 o = 2.7732o5 = 2.7732C5. Another similar convention to denote base-2 exponents

2862-505: The use of either "E" or "D". The ALGOL 60 (1960) programming language uses a subscript ten " 10 " character instead of the letter "E", for example: 6.022 10 23 . This presented a challenge for computer systems which did not provide such a character, so ALGOL W (1966) replaced the symbol by a single quote, e.g. 6.022'+23 , and some Soviet Algol variants allowed the use of the Cyrillic letter " ю ", e.g. 6.022ю+23 . Subsequently,

2916-399: The value and wave shape of the current, after the actual spark event, the quality of the actual combustion process is determined, thus allowing the engine control unit to optimize the timing of the spark for the best engine performance while keeping emissions low on a much wider range of rpms. Since Trionic 7, the throttle and thereby the air charge has also been electronically controlled, but

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