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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 (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, o ...
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 prefix The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
es can be used, which also usually provide steps of a factor of a thousand. 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 A frequency counter is an electronic instrument, or component of one, that is used for measuring frequency. Frequency counters usually measure the number of cycles of oscillation, or pulses per second in a periodic electronic signal. Such an instr ...
by
Hewlett-Packard The Hewlett-Packard Company, commonly shortened to Hewlett-Packard ( ) or HP, was an American multinational information technology company headquartered in Palo Alto, California. HP developed and provided a wide variety of hardware components ...
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-sized ...
to support engineering notation displaying the power-of-ten exponent values was the
HP-25 The HP-25 was a hand-held programmable scientific/engineering calculator made by Hewlett-Packard between early January 1975 and 1978. The HP-25 was introduced as a cheaper ( US$195 MSRP) alternative to the ground-breaking HP-65. To reduce cost ...
in 1975. It was implemented as a dedicated display mode in addition to scientific notation. In 1975,
Commodore Commodore may refer to: Ranks * Commodore (rank), a naval rank ** Commodore (Royal Navy), in the United Kingdom ** Commodore (United States) ** Commodore (Canada) ** Commodore (Finland) ** Commodore (Germany) or ''Kommodore'' * Air 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 technology company headquartered in Dallas, Texas, that designs and manufactures semiconductors and various integrated circuits, which it sells to electronics designers and manufacturers globa ...
calculators of the pre- LCD era such as early SR-40,
TI-30 The TI-30 is a scientific calculator manufactured by Texas Instruments, the first model of which was introduced in 1976. While the original TI-30 was discontinued in 1983 after several design revisions, TI maintains the TI-30 designation as a bran ...
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. ...
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 figure Significant figures (also known as the significant digits, ''precision'' or ''resolution'') of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something. If a number expres ...
s are not always readily apparent when the smallest significant digit or digits are 0. For example, 500 µm and cannot express the
uncertainty Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable ...
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 that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
(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 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. :


Binary engineering notation

Just like decimal engineering notation can be viewed as a base-1000 scientific notation (103 = 1000),
binary Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that ta ...
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 that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can ...
representation ( B notation) commonly used in computer arithmetic, and the usage of IEC
binary prefix A binary prefix is a unit prefix for multiples of units. It is most often used in data processing, data transmission, and digital information, principally in association with the bit and the byte, to indicate multiplication by a power  ...
es, e.g. 1B10 for 1 × 210, 1B20 for 1 × 220, 1B30 for 1 × 230, 1B40 for 1 × 240 etc.


See also

*
Significant figures Significant figures (also known as the significant digits, ''precision'' or ''resolution'') of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something. If a number expres ...
*
Scientific notation Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, o ...
*
Binary prefix A binary prefix is a unit prefix for multiples of units. It is most often used in data processing, data transmission, and digital information, principally in association with the bit and the byte, to indicate multiplication by a power  ...
*
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
(SI) *
RKM code The RKM code, also referred to as "letter and numeral code for resistance and capacitance values and tolerances", "letter and digit code for resistance and capacitance values and tolerances", or informally as "R notation" is a notation to speci ...


Notes


References


External links


Engineering Prefix User Defined Function for Excel

Perl CPAN module for converting number to engineering notation


{{DEFAULTSORT:Engineering Notation Notation, Engineering Numeral systems Notation