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Engineering notation

January 01, 1970

Engineering notation or engineering form (also technical notation) is a version of scientific notation in which the exponent of ten is always selected to be divisible by three to match the common metric prefixes, i.e. scientific notation that aligns with powers of a thousand, for example, 531×103 instead of 5.31×105 (but on calculator displays written without the ×10 to save space). As an alternative to writing powers of 10, SI prefixes can be used,[1] which also usually provide steps of a factor of a thousand.[nb 1] On most calculators, engineering notation is called "ENG" mode as scientific notation is denoted SCI.

History edit

An early implementation of engineering notation in the form of range selection and number display with SI prefixes was introduced in the computerized HP 5360A frequency counter by Hewlett-Packard in 1969.[1]

Based on an idea by Peter D. Dickinson[2][1] the first calculator to support engineering notation displaying the power-of-ten exponent values was the HP-25 in 1975.[3] It was implemented as a dedicated display mode in addition to scientific notation.

In 1975, Commodore introduced a number of scientific calculators (like the SR4148/SR4148R[4] and SR4190R[5]) providing a variable scientific notation, where pressing the EE↓ and EE↑ keys shifted the exponent and decimal point by ±1[nb 2] in scientific notation. Between 1976 and 1980 the same exponent shift facility was also available on some Texas Instruments calculators of the pre-LCD era such as early SR-40,[6][7] TI-30[8][9][10][11][12][13][14][15] and TI-45[16][17] model variants utilizing (INV)EE↓ instead. This can be seen as a precursor to a feature implemented on many Casio calculators since 1978/1979 (e.g. in the FX-501P/FX-502P), where number display in engineering notation is available on demand by the single press of a (INV)ENG button (instead of having to activate a dedicated display mode as on most other calculators), and subsequent button presses would shift the exponent and decimal point of the number displayed by ±3[nb 2] in order to easily let results match a desired prefix. Some graphical calculators (for example the fx-9860G) in the 2000s also support the display of some SI prefixes (f, p, n, μ, m, k, M, G, T, P, E) as suffixes in engineering mode.

Overview edit

Compared to normalized scientific notation, one disadvantage of using SI prefixes and engineering notation is that significant figures are not always readily apparent when the smallest significant digit or digits are 0. For example, 500 μm and 500×10−6 m cannot express the uncertainty distinctions between 5×10−4 m, 5.0×10−4 m, and 5.00×10−4 m. This can be solved by changing the range of the coefficient in front of the power from the common 1–1000 to 0.001–1.0. In some cases this may be suitable; in others it may be impractical. In the previous example, 0.5 mm, 0.50 mm, or 0.500 mm would have been used to show uncertainty and significant figures. It is also common to state the precision explicitly, such as "47 kΩ±5%"

Another example: when the speed of light (exactly 299792458 m/s[18] by the definition of the meter) is expressed as 3.00×108 m/s or 3.00×105 km/s then it is clear that it is between 299500 km/s and 300500 km/s, but when using 300×106 m/s, or 300×103 km/s, 300000 km/s, or the unusual but short 300 Mm/s, this is not clear. A possibility is using 0.300×109 m/s or 0.300 Gm/s.

On the other hand, engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication. For example, 12.5×10−9 m can be read as "twelve-point-five nanometers" (10−9 being nano) and written as 12.5 nm, while its scientific notation equivalent 1.25×10−8 m would likely be read out as "one-point-two-five times ten-to-the-negative-eight meters".

Engineering notation, like scientific notation generally, can use the E notation, such that 3.0×10−9 can be written as 3.0E−9 or 3.0e−9. The E (or e) should not be confused with the Euler's number e or the symbol for the exa-prefix.

SI prefixes
Prefix Representations
Name Symbol Base 1000 Base 10 Value
quetta Q 100010  1030 1000000000000000000000000000000
ronna R 10009  1027 1000000000000000000000000000
yotta Y 10008  1024 1000000000000000000000000
zetta Z 10007  1021 1000000000000000000000
exa E 10006  1018 1000000000000000000
peta P 10005  1015 1000000000000000
tera T 10004  1012 1000000000000
giga G 10003  109 1000000000
mega M 10002  106 1000000
kilo k 10001  103 1000
10000  100 1
milli m 1000−1  10−3 0.001
micro μ 1000−2  10−6 0.000001
nano n 1000−3  10−9 0.000000001
pico p 1000−4  10−12 0.000000000001
femto f 1000−5  10−15 0.000000000000001
atto a 1000−6  10−18 0.000000000000000001
zepto z 1000−7  10−21 0.000000000000000000001
yocto y 1000−8  10−24  0.000000000000000000000001
ronto r 1000−9  10−27  0.000000000000000000000000001
quecto q 1000−10  10−30  0.000000000000000000000000000001

Binary engineering notation edit

Just like decimal engineering notation can be viewed as a base-1000 scientific notation (103 = 1000), binary engineering notation relates to a base-1024 scientific notation (210 = 1024), where the exponent of two must be divisible by ten. This is closely related to the base-2 floating-point representation (B notation) commonly used in computer arithmetic, and the usage of IEC binary prefixes, e.g. 1B10 for 1 × 210, 1B20 for 1 × 220, 1B30 for 1 × 230, 1B40 for 1 × 240 etc.[19]

IEC prefixes
Prefix Representations
Name Symbol Base 1024 Base 2 Value
quebi[nb 3] Qi[nb 3] 102410  2100 1267650600228229401496703205376
robi[nb 3] Ri[nb 3] 10249  290 1237940039285380274899124224
yobi Yi 10248  280 1208925819614629174706176
zebi Zi 10247  270 1180591620717411303424
exbi Ei 10246  260 1152921504606846976
pebi Pi 10245  250 1125899906842624
tebi Ti 10244  240 1099511627776
gibi Gi 10243  230 1073741824
mebi Mi 10242  220 1048576
kibi Ki 10241  210 1024
10240  20 1

See also edit

Notes edit

  1. ^ Except in the case of square and cubic units: in this case the SI prefixes provide only steps of a factor of one million or one billion respectively.
  2. ^ a b One exponent shift action would decrease the exponent by the same amount as the decimal point would be moved to the right, so that the value of the displayed number does not change. Preceding the keypress with INV would inverse the action in the other direction.
  3. ^ a b c d Natural binary counterparts to the ronna- and quetta- decimal prefixes introduced in 2022 were suggested in a consultation paper of the International Committee for Weights and Measures' Consultative Committee for Units (CCU) as robi- (Ri, 10249) and quebi- (Qi, 102410). As of 2022, these binary prefixes have not been adopted by the IEC and ISO.

References edit

  1. ^ a b c Gordon, Gary B.; Reeser, Gilbert A. (May 1969). "Introducing the Computing Counter - Here is the most significant advance in electronic counters in recent years" (PDF). Hewlett-Packard Journal. 20 (9). Hewlett-Packard Company: 2–16. (PDF) from the original on 2017-06-04. Retrieved 2017-06-04. […] Measurements are displayed around a stationary decimal point and the display tubes are grouped in threes to make the display more readable. The numerical display is accompanied by appropriate measurement units (hertz, second, etc.) and a prefix multiplier which is computed by the counter (e.g., k for kilo, M for mega, etc.). There are 12 digital display tubes, to permit shifting the displayed value (11 digits maximum) around the fixed decimal point. Insignificant digits and leading zeros are automatically blanked so only significant digits are displayed, or any number of digits from 3 to 11 can be selected manually. Internally, however, the computer always carries 11 digits. […] (NB. Introduces the HP 5360A Computing Counter.)
  2. ^ US 3987290, Dickinson, Peter D., "Calculator Apparatus for Displaying Data in Engineering Notation", published 1976-10-19, assigned to Hewlett-Packard Company . "[…] A computing counter […] has been developed that displays data in engineering notation with the exponent expressed in alphabetic form rather than in numeric form, such as f in place of −15, p in place of −12, n in place of −9, μ in place of −6, m in place of −3, k in place of +3, M in place of +6, G in place of +9, and T in place of +12. This device, however, is limited to displaying only those numeric quantities for which there exists a commonly accepted alphabetic exponent notation. This device is also limited in the range of data that it can display because the size of the exponent display area is limited, and would be unduly large if required to contain all of the alphabetic characters necessary to represent every exponent that is a multiple of three, for example, in the range −99 to +99. […]" (US 05/578,775)
  3. ^ Neff, Randall B.; Tillman, Lynn (November 1975). "Three New Pocket Calculators: Smaller, less Costly, More Powerful" (PDF). Hewlett-Packard Journal. 27 (3). Hewlett-Packard Company: 1–7. (PDF) from the original on 2017-06-10. Retrieved 2017-06-10. [1]
  4. ^ http://www.wass.net/manuals/Commodore%20SR4148R.pdf [bare URL PDF]
  5. ^ commodore - Multi-Function Preprogrammed Rechargeable Scientific Notation Calculator - Model SR4190R - Owner's Manual (PDF). Commodore. 1975. pp. 10–11. (PDF) from the original on 2017-06-24. Retrieved 2017-06-24. Variable scientific notation: Commodore scientific calculators offer the possibility of changing the exponent at will, therefore allowing the full choice of the unit in which the display may be read. The EE↑ and EE↓ will algebraically increment or decrement the value of the exponent by one for each depression, moving accordingly the decimal point of the mantissa.
  6. ^ "Datamath".
  7. ^ http://www.datamath.net/Manuals/SR-40_US.pdf [bare URL PDF]
  8. ^ "Datamath".
  9. ^ http://www.datamath.net/Manuals/TI-30_1976_US.pdf [bare URL PDF]
  10. ^ "Datamath".
  11. ^ http://www.datamath.net/Manuals/TI-30_BR.pdf [bare URL PDF]
  12. ^ "Datamath".
  13. ^ "Datamath".
  14. ^ "Datamath".
  15. ^ "Datamath".
  16. ^ "Datamath".
  17. ^ http://www.datamath.net/Manuals/TI-45_EU.pdf [bare URL PDF]
  18. ^ "CODATA Value: Speed of light in vacuum c, c0". CODATA 2014: The NIST Reference on Constants, Units, and Uncertainty: Fundamental Physical Constants. NIST. 2017-05-24. from the original on 2017-06-25. Retrieved 2017-05-25.
  19. ^ Martin, Bruce Alan (October 1968). "Letters to the editor: On binary notation". Communications of the ACM. 11 (10). Associated Universities Inc.: 658. doi:10.1145/364096.364107. S2CID 28248410.

External links edit

  • Engineering Prefix User Defined Function for Excel
  • Perl CPAN module for converting number to engineering notation
  • Java functions for converting between a string and a double type

January 01, 1970
engineering, notation, engineering, form, also, technical, notation, version, scientific, notation, which, exponent, always, selected, divisible, three, match, common, metric, prefixes, scientific, notation, that, aligns, with, powers, thousand, example, inste. Engineering notation or engineering form also technical notation is a version of scientific notation in which the exponent of ten is always selected to be divisible by three to match the common metric prefixes i e scientific notation that aligns with powers of a thousand for example 531 103 instead of 5 31 105 but on calculator displays written without the 10 to save space As an alternative to writing powers of 10 SI prefixes can be used 1 which also usually provide steps of a factor of a thousand nb 1 On most calculators engineering notation is called ENG mode as scientific notation is denoted SCI Contents 1 History 2 Overview 3 Binary engineering notation 4 See also 5 Notes 6 References 7 External linksHistory editAn early implementation of engineering notation in the form of range selection and number display with SI prefixes was introduced in the computerized HP 5360A frequency counter by Hewlett Packard in 1969 1 Based on an idea by Peter D Dickinson 2 1 the first calculator to support engineering notation displaying the power of ten exponent values was the HP 25 in 1975 3 It was implemented as a dedicated display mode in addition to scientific notation In 1975 Commodore introduced a number of scientific calculators like the SR4148 SR4148R 4 and SR4190R 5 providing a variable scientific notation where pressing the EE and EE keys shifted the exponent and decimal point by 1 nb 2 in scientific notation Between 1976 and 1980 the same exponent shift facility was also available on some Texas Instruments calculators of the pre LCD era such as early SR 40 6 7 TI 30 8 9 10 11 12 13 14 15 and TI 45 16 17 model variants utilizing INV EE instead This can be seen as a precursor to a feature implemented on many Casio calculators since 1978 1979 e g in the FX 501P FX 502P where number display in engineering notation is available on demand by the single press of a INV ENG button instead of having to activate a dedicated display mode as on most other calculators and subsequent button presses would shift the exponent and decimal point of the number displayed by 3 nb 2 in order to easily let results match a desired prefix Some graphical calculators for example the fx 9860G in the 2000s also support the display of some SI prefixes f p n m m k M G T P E as suffixes in engineering mode Overview editThis section does not cite any sources Please help improve this section by adding citations to reliable sources Unsourced material may be challenged and removed February 2024 Learn how and when to remove this message Compared to normalized scientific notation one disadvantage of using SI prefixes and engineering notation is that significant figures are not always readily apparent when the smallest significant digit or digits are 0 For example 500 mm and 500 10 6 m cannot express the uncertainty distinctions between 5 10 4 m 5 0 10 4 m and 5 00 10 4 m This can be solved by changing the range of the coefficient in front of the power from the common 1 1000 to 0 001 1 0 In some cases this may be suitable in others it may be impractical In the previous example 0 5 mm 0 50 mm or 0 500 mm would have been used to show uncertainty and significant figures It is also common to state the precision explicitly such as 47 kW 5 Another example when the speed of light exactly 299792 458 m s 18 by the definition of the meter is expressed as 3 00 108 m s or 3 00 105 km s then it is clear that it is between 299500 km s and 300500 km s but when using 300 106 m s or 300 103 km s 300000 km s or the unusual but short 300 Mm s this is not clear A possibility is using 0 300 109 m s or 0 300 Gm s On the other hand engineering notation allows the numbers to explicitly match their corresponding SI prefixes which facilitates reading and oral communication For example 12 5 10 9 m can be read as twelve point five nanometers 10 9 being nano and written as 12 5 nm while its scientific notation equivalent 1 25 10 8 m would likely be read out as one point two five times ten to the negative eight meters Engineering notation like scientific notation generally can use the E notation such that 3 0 10 9 can be written as 3 0E 9 or 3 0e 9 The E or e should not be confused with the Euler s number e or the symbol for the exa prefix SI prefixes Prefix Representations Name Symbol Base 1000 Base 10 Value quetta Q 100010 1030 1000 000 000 000 000 000 000 000 000 000 ronna R 10009 1027 1000 000 000 000 000 000 000 000 000 yotta Y 10008 1024 1000 000 000 000 000 000 000 000 zetta Z 10007 1021 1000 000 000 000 000 000 000 exa E 10006 1018 1000 000 000 000 000 000 peta P 10005 1015 1000 000 000 000 000 tera T 10004 1012 1000 000 000 000 giga G 10003 109 1000 000 000 mega M 10002 106 1000 000 kilo k 10001 103 1000 10000 100 1 milli m 1000 1 10 3 0 001 micro m 1000 2 10 6 0 000001 nano n 1000 3 10 9 0 000000 001 pico p 1000 4 10 12 0 000000 000 001 femto f 1000 5 10 15 0 000000 000 000 001 atto a 1000 6 10 18 0 000000 000 000 000 001 zepto z 1000 7 10 21 0 000000 000 000 000 000 001 yocto y 1000 8 10 24 0 000000 000 000 000 000 000 001 ronto r 1000 9 10 27 0 000000 000 000 000 000 000 000 001 quecto q 1000 10 10 30 0 000000 000 000 000 000 000 000 000 001Binary engineering notation editJust like decimal engineering notation can be viewed as a base 1000 scientific notation 103 1000 binary engineering notation relates to a base 1024 scientific notation 210 1024 where the exponent of two must be divisible by ten This is closely related to the base 2 floating point representation B notation commonly used in computer arithmetic and the usage of IEC binary prefixes e g 1B10 for 1 210 1B20 for 1 220 1B30 for 1 230 1B40 for 1 240 etc 19 IEC prefixes Prefix Representations Name Symbol Base 1024 Base 2 Value quebi nb 3 Qi nb 3 102410 2100 1267 650 600 228 229 401 496 703 205 376 robi nb 3 Ri nb 3 10249 290 1237 940 039 285 380 274 899 124 224 yobi Yi 10248 280 1208 925 819 614 629 174 706 176 zebi Zi 10247 270 1180 591 620 717 411 303 424 exbi Ei 10246 260 1152 921 504 606 846 976 pebi Pi 10245 250 1125 899 906 842 624 tebi Ti 10244 240 1099 511 627 776 gibi Gi 10243 230 1073 741 824 mebi Mi 10242 220 1048 576 kibi Ki 10241 210 1024 10240 20 1See also editSignificant figures Scientific notation Binary prefix International System of Units SI RKM codeNotes edit Except in the case of square and cubic units in this case the SI prefixes provide only steps of a factor of one million or one billion respectively a b One exponent shift action would decrease the exponent by the same amount as the decimal point would be moved to the right so that the value of the displayed number does not change Preceding the keypress with INV would inverse the action in the other direction a b c d Natural binary counterparts to the ronna and quetta decimal prefixes introduced in 2022 were suggested in a consultation paper of the International Committee for Weights and Measures Consultative Committee for Units CCU as robi Ri 10249 and quebi Qi 102410 As of 2022 update these binary prefixes have not been adopted by the IEC and ISO References edit a b c Gordon Gary B Reeser Gilbert A May 1969 Introducing the Computing Counter Here is the most significant advance in electronic counters in recent years PDF Hewlett Packard Journal 20 9 Hewlett Packard Company 2 16 Archived PDF from the original on 2017 06 04 Retrieved 2017 06 04 Measurements are displayed around a stationary decimal point and the display tubes are grouped in threes to make the display more readable The numerical display is accompanied by appropriate measurement units hertz second etc and a prefix multiplier which is computed by the counter e g k for kilo M for mega etc There are 12 digital display tubes to permit shifting the displayed value 11 digits maximum around the fixed decimal point Insignificant digits and leading zeros are automatically blanked so only significant digits are displayed or any number of digits from 3 to 11 can be selected manually Internally however the computer always carries 11 digits NB Introduces the HP 5360A Computing Counter US 3987290 Dickinson Peter D Calculator Apparatus for Displaying Data in Engineering Notation published 1976 10 19 assigned to Hewlett Packard Company A computing counter has been developed that displays data in engineering notation with the exponent expressed in alphabetic form rather than in numeric form such as f in place of 15 p in place of 12 n in place of 9 m in place of 6 m in place of 3 k in place of 3 M in place of 6 G in place of 9 and T in place of 12 This device however is limited to displaying only those numeric quantities for which there exists a commonly accepted alphabetic exponent notation This device is also limited in the range of data that it can display because the size of the exponent display area is limited and would be unduly large if required to contain all of the alphabetic characters necessary to represent every exponent that is a multiple of three for example in the range 99 to 99 US 05 578 775 Neff Randall B Tillman Lynn November 1975 Three New Pocket Calculators Smaller less Costly More Powerful PDF Hewlett Packard Journal 27 3 Hewlett Packard Company 1 7 Archived PDF from the original on 2017 06 10 Retrieved 2017 06 10 1 http www wass net manuals Commodore 20SR4148R pdf bare URL PDF commodore Multi Function Preprogrammed Rechargeable Scientific Notation Calculator Model SR4190R Owner s Manual PDF Commodore 1975 pp 10 11 Archived PDF from the original on 2017 06 24 Retrieved 2017 06 24 Variable scientific notation Commodore scientific calculators offer the possibility of changing the exponent at will therefore allowing the full choice of the unit in which the display may be read The EE and EE will algebraically increment or decrement the value of the exponent by one for each depression moving accordingly the decimal point of the mantissa Datamath http www datamath net Manuals SR 40 US pdf bare URL PDF Datamath http www datamath net Manuals TI 30 1976 US pdf bare URL PDF Datamath http www datamath net Manuals TI 30 BR pdf bare URL PDF Datamath Datamath Datamath Datamath Datamath http www datamath net Manuals TI 45 EU pdf bare URL PDF CODATA Value Speed of light in vacuum c c0 CODATA 2014 The NIST Reference on Constants Units and Uncertainty Fundamental Physical Constants NIST 2017 05 24 Archived from the original on 2017 06 25 Retrieved 2017 05 25 Martin Bruce Alan October 1968 Letters to the editor On binary notation Communications of the ACM 11 10 Associated Universities Inc 658 doi 10 1145 364096 364107 S2CID 28248410 External links editEngineering Prefix User Defined Function for Excel Perl CPAN module for converting number to engineering notation Java functions for converting between a string and a double type Retrieved from https en wikipedia org w index php title Engineering notation amp oldid 1223282349 Exponent shift, wikipedia, wiki, book, books, library,

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