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Engineering notation or engineering form is a version of scientific notation in which the exponent of ten must be divisible by three (i.e., they are powers of a thousand, but written as, for example, 106 instead of 10002). 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.

History

An early implementation of engineering notation in 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]On most calculators, engineering notation is called "ENG" mode.

An early implementation of engineering notation in 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 [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 about 1978/1979 (f.e. 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.

Compared to normalized scientific notation, one disadvantage of using SI prefixes and engineering notation is that significant figures are not always readily apparent. 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/sspeed of light (exactly 299792458 m/s[18] by the definition of the meter and second) is expressed as 3.00 × 108 m/s or 3.00 × 105 km/s then it is clear that it is between 299 500 km/s and 300 500 km/s, but when using 300 × 106 m/s, or 300 × 103 km/s, 300 000 km/s, or the unusual but short 300 Mm/s, this is not clear. A possibility is using 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" 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

can be written as

3.0E−9 (or 3.0e−9)
The E (or e) should not be confused with the exponential e which holds a completely different significance. In the latter case, it would be shown that 3e−9 ≈ 0.000 370 23.

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.

References

  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. Hewlett-Packard Company. 20 (9): 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 (e.g., Hz, Sec, 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. […]