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Engineering notation
From Wikipedia, the free encyclopedia
Engineering notation is 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 e.g. 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 | Short scale | Long scale | Decimal equivalent in SI writing style |
|---|---|---|---|---|---|---|
| 10008 | 1024 | yotta | Y | Septillion | Quadrillion | 1 000 000 000 000 000 000 000 000 |
| 10007 | 1021 | zetta | Z | Sextillion | Trilliard (thousand trillion) | 1 000 000 000 000 000 000 000 |
| 10006 | 1018 | exa | E | Quintillion | Trillion | 1 000 000 000 000 000 000 |
| 10005 | 1015 | peta | P | Quadrillion | Billiard (thousand billion) | 1 000 000 000 000 000 |
| 10004 | 1012 | tera | T | Trillion | Billion | 1 000 000 000 000 |
| 10003 | 109 | giga | G | Billion | Milliard (thousand million) | 1 000 000 000 |
| 10002 | 106 | mega | M | Million | 1 000 000 | |
| 10001 | 103 | kilo | k | Thousand | 1 000 | |
| 10002/3 | 102 | hecto | h | Hundred | 100 | |
| 10001/3 | 101 | deca, deka | da | Ten | 10 | |
| 10000 | 100 | (none) | (none) | One | 1 | |
| 1000−1/3 | 10−1 | deci | d | Tenth | 0.1 | |
| 1000−2/3 | 10−2 | centi | c | Hundredth | 0.01 | |
| 1000−1 | 10−3 | milli | m | Thousandth | 0.001 | |
| 1000−2 | 10−6 | micro | µ (u) | Millionth | 0.000 001 | |
| 1000−3 | 10−9 | nano | n | Billionth | Milliardth | 0.000 000 001 |
| 1000−4 | 10−12 | pico | p | Trillionth | Billionth | 0.000 000 000 001 |
| 1000−5 | 10−15 | femto | f | Quadrillionth | Billiardth | 0.000 000 000 000 001 |
| 1000−6 | 10−18 | atto | a | Quintillionth | Trillionth | 0.000 000 000 000 000 001 |
| 1000−7 | 10−21 | zepto | z | Sextillionth | Trilliardth | 0.000 000 000 000 000 000 001 |
| 1000−8 | 10−24 | yocto | y | Septillionth | Quadrillionth | 0.000 000 000 000 000 000 000 001 |
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