# 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).

Metric prefixes
PrefixSymbol1000m10nDecimalShort scaleLong scaleSince[n 1]
zettaZ1000710211000000000000000000000sextilliontrilliard1991
exaE1000610181000000000000000000quintilliontrillion1975
teraT1000410121000000000000trillionbillion1960
gigaG100031091000000000billionmilliard1960
megaM100021061000000million1960
kilok100011031000thousand1795
hectoh10002/3102100hundred1795
100001001one
decid1000−1/310−10.1tenth1795
centic1000−2/310−20.01hundredth1795
millim1000−110−30.001thousandth1795
microμ1000−210−60.000001millionth1960
nanon1000−310−90.000000001billionthmilliardth1960
picop1000−410−120.000000000001trillionthbillionth1960
attoa1000−610−180.000000000000000001quintillionthtrillionth1964
zeptoz1000−710−210.000000000000000000001sextillionthtrilliardth1991
1. ^ The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM.

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 ≈ 0.001 006.