Engineering notation

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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).

SI prefixes

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

[edit] See also

• SI
• Significant figures