Engineering notation
Encyclopedia
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 1,0002). As an alternative to writing powers of 10, SI prefix
es can be used, which also usually provide steps of a factor of a thousand.
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 1–1,000 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, 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.
Scientific notation
Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in standard decimal notation. Scientific notation has a number of useful properties and is commonly used in calculators and by scientists, mathematicians, doctors, and engineers.In scientific...
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 1,0002). As an alternative to writing powers of 10, SI prefix
SI prefix
The International System of Units specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decadic multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol...
es can be used, which also usually provide steps of a factor of a thousand.
Compared to normalized scientific notation, one disadvantage of using SI prefixes and engineering notation is that significant figures
Significant figures
The significant figures of a number are those digits that carry meaning contributing to its precision. This includes all digits except:...
are not always readily apparent. For example, 500 µm and 500 × 10−6 m cannot express the uncertainty
Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...
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 1–1,000 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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
(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, 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
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
which holds a completely different significance. In the latter case, it would be shown that 3e−8 = 0.001006.