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).
| 1000n | 10n | Prefix | Symbol | Since[1] | Short scale | Long scale | Decimal equivalent in SI writing style |
|---|---|---|---|---|---|---|---|
| 10008 | 1024 | yotta- | Y | 1991 | Septillion | Quadrillion | 1 000 000 000 000 000 000 000 000 |
| 10007 | 1021 | zetta- | Z | 1991 | Sextillion | Trilliard (thousand trillion) | 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 (thousand billion) | 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 (thousand million) | 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 |
| Notes: 1. The 1795 dates identify prefixes in use since the metric system was introduced. The other dates are not necessarily dates of first use, but rather the date of recognition by a resolution of the CGPM, which first met in 1889. 2. The micron was earlier recognized by the CGPM in 1948; that decision was abrogated in 1967-68. | |||||||
Engineering Notation, as used in Civil and Mechanical Engineering (United States), uses the following notation where:
(Note: The following example is in scientific notation, not Engineering notation, where the exponent is required to be a multiple of 3)
3.0×10-8
can be written as
3.0E-8 or 3.0e-8
This is a common terminology for reporting values with a given significance (i.e. significant digits) in practical/common situations. 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
in cartesian coordinates.
[edit] See also
