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

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 scientif ...

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 in

E 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 scienti ...

- with "E" instead of "×10" to save space). As an alternative to writing powers of 10,

SI prefix The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...

es can be used, which also usually provide steps of a factor of a thousand. 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 The Hewlett-Packard Company, commonly shortened to Hewlett-Packard ( ) or HP, was an American multinational information technology company. It was founded by Bill Hewlett and David Packard in 1939 in a one-car garage in Palo Alto, California ...

in 1969. Based on an idea by Peter D. Dickinson the first

calculator An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics. The first solid-state electronic calculator was created in the early 1960s. Pocket-si ...

to support engineering notation displaying the power-of-ten exponent values was the HP-25 in 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 and SR4190R) providing a ''variable scientific notation'', where pressing the and keys shifted the exponent and decimal point by ±1 in ''scientific'' notation. Between 1976 and 1980 the same ''exponent shift'' facility was also available on some

Texas Instruments Texas Instruments Incorporated (TI) is an American multinational semiconductor company headquartered in Dallas, Texas. It is one of the top 10 semiconductor companies worldwide based on sales volume. The company's focus is on developing analog ...

calculators of the pre- LCD era such as early SR-40, TI-30 and TI-45 model variants utilizing () instead. This can be seen as a precursor to a feature implemented on many

Casio is a Japanese multinational electronics manufacturing corporation headquartered in Shibuya, Tokyo, Japan. Its products include calculators, mobile phones, digital cameras, electronic musical instruments, and analogue and digital watches. It ...

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 () 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 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

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 cannot express the

uncertainty Uncertainty or incertitude refers to situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown, and is particularly relevant for decision ...

distinctions between , , and . 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 "" Another example: when the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

(exactly by the definition of the meter) is expressed as or then it is clear that it is between and , but when using , or , , or the unusual but short , this is not clear. A possibility is using or . On the other hand, engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication. For example, can be read as "twelve-point-five nanometers" (10⁻⁹ being ''nano'') and written as 12.5 nm, while its scientific notation equivalent 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

, such that 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. :

Binary engineering notation

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 In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that ba ...

representation ( B notation) commonly used in computer arithmetic, and the usage of IEC

binary prefix A binary prefix is a unit prefix that indicates a multiple of a unit of measurement by an integer power of two. The most commonly used binary prefixes are kibi (symbol Ki, meaning ), mebi (), and gibi (). They are most often used in inform ...

es, e.g. 1B10 for 1 × 2¹⁰, 1B20 for 1 × 2²⁰, 1B30 for 1 × 2³⁰, 1B40 for 1 × 2⁴⁰ etc.

Notes

References

External links