engineering notation

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).

Engineering Notation, as used in Civil and Mechanical Engineering (United States), uses the following notation where:

(Note: The following example is in scientific notation, not Engineering notation, where the exponent is required to be a multiple of 3)

3.0×10^-8

can be written as

3.0E^-8 or 3.0e^-8

This is a common terminology for reporting values with a given significance (i.e. significant digits) in practical/common situations. 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

in cartesian coordinates.

See also

• SI
• Significant figures

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