Engineering notation
Template:Short description Template:Use dmy dates Template:Use list-defined references
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,<ref name="Gordon_1969"/> which also usually provide steps of a factor of a thousand.<ref group="nb" name="NB_Cubic"/> On most calculators, engineering notation is called "ENG" mode as scientific notation is denoted SCI.
Template:AnchorHistoryEdit
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.<ref name="Gordon_1969"/>
Based on an idea by Peter D. Dickinson<ref name="Dickinson_1976"/><ref name="Gordon_1969"/> the first calculator to support engineering notation displaying the power-of-ten exponent values was the HP-25 in 1975.<ref name="Neff_1975"/> 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<ref name="Commodore_SR4148R"/> and SR4190R<ref name="Commodore_SR4190R"/>) providing a variable scientific notation, where pressing the Template:Button and Template:Button keys shifted the exponent and decimal point by ±1<ref group="nb" name="NB_Exp-Shift"/> 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,<ref name="SR-40"/><ref name="SR-40_Manual"/> TI-30<ref name="TI-30"/><ref name="TI-30_Manual"/><ref name="TI-30-BR"/><ref name="TI-30_BR_Manual"/><ref name="TI-30_2"/><ref name="TI-30_RCI"/><ref name="TI-30_1"/><ref name="TI-30_Super"/> and TI-45<ref name="TI-45"/><ref name="TI-45_Manual"/> model variants utilizing (Template:Button)Template:Button 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 (Template:Button)Template:Button 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<ref group="nb" name="NB_Exp-Shift"/> 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.
OverviewEdit
Template:Uncited section 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 Template:Val cannot express the uncertainty distinctions between Template:Val, Template:Val, and Template:Val. 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 "Template:Gaps"
Another example: when the speed of light (exactly Template:Val<ref name="CUU_2014_c"/> by the definition of the meter) is expressed as Template:Val or Template:Val then it is clear that it is between Template:Val and Template:Val, but when using Template:Val, or Template:Val, Template:Val, or the unusual but short Template:Val, this is not clear. A possibility is using Template:Val or Template:Val.
On the other hand, engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication. For example, Template:Val can be read as "twelve-point-five nanometers" (10−9 being nano) and written as 12.5 nm, while its scientific notation equivalent Template:Val 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 Template:Val 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 Template:Val ronna R 10009 1027 Template:Val yotta Y 10008 1024 Template:Val zetta Z 10007 1021 Template:Val exa E 10006 1018 Template:Val peta P 10005 1015 Template:Val tera T 10004 1012 Template:Val giga G 10003 109 Template:Val mega M 10002 106 Template:Val kilo k 10001 103 Template:Val 10000 100 1 milli m 1000−1 10−3 Template:Val micro μ 1000−2 10−6 Template:Val nano n 1000−3 10−9 Template:Val pico p 1000−4 10−12 Template:Val femto f 1000−5 10−15 Template:Val atto a 1000−6 10−18 Template:Val zepto z 1000−7 10−21 Template:Val yocto y 1000−8 10−24 Template:Val ronto r 1000−9 10−27 Template:Val quecto q 1000−10 10−30 Template:Val
Template:AnchorBinary engineering notationEdit
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.<ref name="Martin_1968"/>
| IEC prefixes | ||||
|---|---|---|---|---|
| Prefix | Representations | |||
| Name | Symbol | Base 1024 | Base 2 | Value |
| quebi<ref group="nb" name="NB_NewBinPrefix"/> | Qi<ref group="nb" name="NB_NewBinPrefix"/> | 102410 | 2100 | Template:Val |
| robi<ref group="nb" name="NB_NewBinPrefix"/> | Ri<ref group="nb" name="NB_NewBinPrefix"/> | 10249 | 290 | Template:Val |
| yobi | Yi | 10248 | 280 | Template:Val |
| zebi | Zi | 10247 | 270 | Template:Val |
| exbi | Ei | 10246 | 260 | Template:Val |
| pebi | Pi | 10245 | 250 | Template:Val |
| tebi | Ti | 10244 | 240 | Template:Val |
| gibi | Gi | 10243 | 230 | Template:Val |
| mebi | Mi | 10242 | 220 | Template:Val |
| kibi | Ki | 10241 | 210 | Template:Val |
| 10240 | 20 | Template:Val | ||