Engineering notation

Source: Wikipedia, the free encyclopedia.

Engineering notation or engineering form (also technical notation) is a version of

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

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,

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

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

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

Just like decimal engineering notation can be viewed as a base-1000 scientific notation (103 = 1000),

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

Notes

  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. ^
    quebi- (Qi, 102410). As of 2022
    , these binary prefixes have not been adopted by the IEC and ISO.

References

  1. ^
    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.)
  2. 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. Hewlett-Packard Company: 1–7. Archived (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
    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. NIST. 2017-05-24. Archived
    from the original on 2017-06-25. Retrieved 2017-05-25.
  19. S2CID 28248410
    .

External links
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