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
The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM. 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.

[edit] 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

[edit] See also

• SI
• Significant figures