Engineering notation

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Engineering notation is a version of scientific notation in which the power of ten must be a multiple of three (i.e, they are powers of a thousand, but written as, for example, 106 instead of 1,0002). As an alternative to writing powers of 10, SI prefixes can be used, which also usually provide steps of a factor of a thousand.1

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, 5.0 × 10−4, and 5.00 × 10−4 m. This can be solved by the changing the range of the coefficient in front of the power from the common 1–1,000 to 0.01–10 . In some cases this may be suitable; in others it may be impractical. In the previous example we would have used 0.5, 0.50, or 0.500 mm to show uncertainty and significant figures.

Another example: when the speed of light (defined as 299,792,458 m/s) is expressed as 3.00 × 108 m/s or 3.00 × 105 km/s then it is clear that it is between 299,500 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).

SI prefixes
1000m 10n Prefix Symbol Since[1] Short scale Long scale Decimal
10008 1024 yotta- Y 1991 Septillion Quadrillion 1 000 000 000 000 000 000 000 000
10007 1021 zetta- Z 1991 Sextillion Trilliard 1 000 000 000 000 000 000 000
10006 1018 exa- E 1975 Quintillion Trillion 1 000 000 000 000 000 000
10005 1015 peta- P 1975 Quadrillion Billiard 1 000 000 000 000 000
10004 1012 tera- T 1960 Trillion Billion 1 000 000 000 000
10003 109 giga- G 1960 Billion Milliard 1 000 000 000
10002 106 mega- M 1960 Million 1 000 000
10001 103 kilo- k 1795 Thousand 1 000
10002/3 102 hecto- h 1795 Hundred 100
10001/3 101 deca- da 1795 Ten 10
10000 100 (none) (none) NA One 1
1000−1/3 10−1 deci- d 1795 Tenth 0.1
1000−2/3 10−2 centi- c 1795 Hundredth 0.01
1000−1 10−3 milli- m 1795 Thousandth 0.001
1000−2 10−6 micro- µ 1960[2] Millionth 0.000 001
1000−3 10−9 nano- n 1960 Billionth Milliardth 0.000 000 001
1000−4 10−12 pico- p 1960 Trillionth Billionth 0.000 000 000 001
1000−5 10−15 femto- f 1964 Quadrillionth Billiardth 0.000 000 000 000 001
1000−6 10−18 atto- a 1964 Quintillionth Trillionth 0.000 000 000 000 000 001
1000−7 10−21 zepto- z 1991 Sextillionth Trilliardth 0.000 000 000 000 000 000 001
1000−8 10−24 yocto- y 1991 Septillionth Quadrillionth 0.000 000 000 000 000 000 000 001
  1. The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM.
  2. The 1948 recognition of the micron by the CGPM was abrogated in 1967.


Engineering notation, as used in civil and mechanical engineering (United States), uses the following notation where:

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−8 = 0.001006.

Notes

  1. ^ Except in the case of square and cubic units: in this case the SI prefixes provide only steps of a factor one million or one billion

See also

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  • This page was last modified on 22 December 2008, at 17:50.

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