Engineering notation

Engineering notation is a version of scientific notation in which the powers of ten must be multiples of 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 prefixes can be used, which also usually provide steps of a factor of a thousand.

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 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, 0.50, 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 299 792 458 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 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).

Metric prefixes

Prefix Symbol 1000m 10n Decimal English word Since yotta Y  10008  1024 1000000000000000000000000 septillion 1991 zetta Z  10007  1021 1000000000000000000000 sextillion 1991 exa E  10006  1018 1000000000000000000 quintillion 1975 peta P  10005  1015 1000000000000000 quadrillion 1975 tera T  10004  1012 1000000000000 trillion 1960 giga G  10003  109 1000000000 billion 1960 mega M  10002  106 1000000 million 1960 kilo k  10001  103 1000 thousand 1795 hecto h  10002/3  102 100 hundred 1795 deca da  10001/3  101 10 ten 1795  10000  100 1 one – deci d  1000−1/3  10−1 0.1 tenth 1795 centi c  1000−2/3   10−2 0.01 hundredth 1795 milli m  1000−1  10−3 0.001 thousandth 1795 micro µ  1000−2  10−6 0.000001 millionth 1960 nano n  1000−3  10−9 0.000000001 billionth 1960 pico p  1000−4  10−12 0.000000000001 trillionth 1960 femto f  1000−5  10−15 0.000000000000001 quadrillionth 1964 atto a  1000−6  10−18 0.000000000000000001 quintillionth 1964 zepto z  1000−7  10−21 0.000000000000000000001 sextillionth 1991 yocto y  1000−8  10−24  0.000000000000000000000001 septillionth 1991

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⁻⁹ ≈ 0.001 006.

See also

• SI
• Significant figures
• Scientific notation

External links

• Perl CPAN module for converting number to engineering notation
• Java functions for converting between a string and a double type