# 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).[1] As an alternative to writing powers of 10, SI prefixes can be used, which also usually provide steps of a factor of a thousand.[2]

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).

Engineering notation, like scientific notation generally, can use the E notation, such that

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 ≈ 0.000 370 23.

Metric prefixes
PrefixSymbol1000m10nDecimalEnglish wordSince[n 1]
short scalelong scale
zettaZ 10007 10211000000000000000000000 sextillion thousand trillion1991
exaE 10006 10181000000000000000000 quintillion trillion1975
petaP 10005 10151000000000000000 quadrillion thousand billion1975
teraT 10004 10121000000000000 trillion billion1960
gigaG 10003 1091000000000 billion thousand million1960
megaM 10002 1061000000            million1960
kilok 10001 1031000            thousand1795
hectoh 10002/3 102100            hundred1795
10000 1001            one
decid 1000−1/3 10−10.1            tenth1795
centic 1000−2/3  10−20.01            hundredth1795
millim 1000−1 10−30.001            thousandth1795
microµ 1000−2 10−60.000001            millionth1960
nanon 1000−3 10−90.000000001 billionth thousand millionth1960
picop 1000−4 10−120.000000000001 trillionth billionth1960
femtof 1000−5 10−150.000000000000001 quadrillionth thousand billionth1964
attoa 1000−6 10−180.000000000000000001 quintillionth trillionth1964
zeptoz 1000−7 10−210.000000000000000000001 sextillionth thousand trillionth1991
yoctoy 1000−8 10−24 0.000000000000000000000001 septillionth quadrillionth 1991
1. ^ The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM.