Engineering notation

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Engineering notation 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).[1] As an alternative to writing powers of 10, SI prefixes can be used, which also usually provide steps of a factor of a thousand.[2] On calculators, engineering notation is named "ENG".

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/s 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/2 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, convenient to write, but somewhat impractical in understanding (writing something large as a fraction of something even larger; in a context of larger numbers expressed in the same unit this could be convenient, but that is not applicable here).

Engineering notation, like scientific notation generally, can use the E notation, such that

3.0 × 10−9

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.

Prefix 1000m 10n Decimal English word Since[nb 1]
Name Symbol Short scale Long scale
yotta Y  10008  1024 1000000000000000000000000  septillion  quadrillion 1991
zetta Z  10007  1021 1000000000000000000000  sextillion  thousand trillion 1991
exa E  10006  1018 1000000000000000000  quintillion  trillion 1975
peta P  10005  1015 1000000000000000  quadrillion  thousand billion 1975
tera T  10004  1012 1000000000000  trillion  billion 1960
giga G  10003  109 1000000000  billion  thousand million 1960
mega M  10002  106 1000000             million 1960 (1873)
kilo k  10001  103 1000             thousand 1960 (1795)
hecto h  10002/3  102 100             hundred 1960 (1795)
deca da  10001/3  101 10             ten 1960 (1795)
 10000  100 1             one
deci d  1000−1/3  10−1 0.1             tenth 1960 (1795)
centi c  1000−2/3   10−2 0.01             hundredth 1960 (1795)
milli m  1000−1  10−3 0.001             thousandth 1960 (1795)
micro μ  1000−2  10−6 0.000001             millionth 1960 (1873)
nano n  1000−3  10−9 0.000000001  billionth  thousand millionth 1960
pico p  1000−4  10−12 0.000000000001  trillionth  billionth 1960
femto f  1000−5  10−15 0.000000000000001  quadrillionth  thousand billionth 1964
atto a  1000−6  10−18 0.000000000000000001  quintillionth  trillionth 1964
zepto z  1000−7  10−21 0.000000000000000000001  sextillionth  thousand trillionth 1991
yocto y  1000−8  10−24  0.000000000000000000000001  septillionth  quadrillionth  1991
  1. ^ The metric system was introduced in 1795 with several metric prefixes, of which, however, only six were adopted as SI prefixes by the 11th CGPM conference in 1960, whereas myria (ma, 104) and myrio (mo, 10-4) as well as double and demi were not adopted. In 1873, micro and mega were recommended by the British Association for the Advancement of Science. The other dates relate to recognition by a resolution of the CGPM.

See also[edit]

Notes[edit]

  1. ^ US 3987290, Dickinson, Peter D., "Calculator Apparatus for Displaying Data in Engineering Notation", issued Oct. 19, 1976 
  2. ^ 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.

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