Scientific notation
As scientific notation (English: scientific notation ) refers to two varieties of modern numerical representation: the exponential, and traditional scientific notation or standard representation called, and engineering notation (English: engineering notation ). In both The numerical value is split into mantissa and exponent ( base 10):
Here, a point number (with additional conditions ), an integer.
- The traditional scientific notation is discussed in detail in the article exponential. This always has only one non-zero, the left side decimal so. The advantage is in the science of rapid overview of the magnitude and possibly comparison of several numerical values. Usually a number is specified in the format. The disadvantage of this notation format is that in practice, the results have to be mostly " nachformatiert " to use with SI units of symbols or to be able to express in the naming system as numbers.
- In the technical notation as exponents only integer multiples of 3 are used, so integer powers of thousand. ( Then is usually in the range. ) So this is a notation on the use of units of measurement, because in these the standardized scales ( micro, milli, kilo, mega, and so on ) correspond to powers of 103.
Scientific Calculator
Most modern calculators can automatically numbers in scientific notation display (display shows for example: SCI). For very large numbers or very small decimal fractions, this is usually not otherwise possible anyway.
The term scientific notation is, however, not used very uniform, but very often also easy - especially in English - synonymously with the traditional scientific notation - ie for exponential notation - used. On calculators engineering notation usually with ENG (engineering notation ) is called.
If no superscript numbers are available, the following notation is used: from 1.1018 is 1 E18. The number 3200, for example, can thus be also listed 3,200 E3. ( See also exponential )
Precision in the SI and ENG Format
Sometimes both the SI - orders of magnitude as well as the engineer format was accused of casting doubt on the accuracy of the determined values .
In fact, the exponential is a very simple and clear way the precision of the results again, namely by the number of nachstelligen digits. For example, the results do not mean 5 E -4 m, 5.0 m and 5.00 E-4 E-4 m just the same. These three different results, but would have to be reduced indiscriminately to 500 microns or 500 E-6 m in both the SI and the ENG format.
This apparent shortcoming of the SI and ENG format can be canceled by the results are expressed as decimal fractions of the higher order, in the above example, each as 0.5 mm, 0.50 mm and 0.500 mm or 0.5 E -3 m, 0.50 m and 0.500 e-3 e-3 m. The indication of the accuracy is restored. This approach is in any case only to not more than two decimal detectable results required a rather rare case in science.