Scientific notation

Scientific notation refers to two variants of modern number notation: exponential notation, also known as traditional scientific notation or standard notation, and engineering notation. In both, the numerical value to be represented is divided into mantissa and exponent (base 10):

Here the mantissa is a decimal number (with additional conditions), the exponent is an integer.

Here always has only one non-zero left decimal place, i.e. . The advantage in science is the quick overview of the magnitude and the possible comparison of several numerical values. Usually, a number is given in the format . The disadvantage of this notation format is that the results must be "reformatted" if they are to be expressed using the prefixes of the SI symbol units.

Scientific calculators

Most modern calculators can automatically display numbers in scientific notation (e.g. SCI). With very large numbers or very small decimal fractions, this is usually not possible in any other way anyway.

However, the term scientific notation is not used quite uniformly, but is very often simply used - especially in English - as a synonym for traditional scientific notation - i.e. exponential notation. On pocket calculators, technical notation is usually designated ENG (engineering notation).

If no superscript digits are available, the following notation is used: 1-1018 becomes 1 E18. The number 3200, for example, can thus also be written 3.2 E3. (See also exponential representation)

Precision in SI and ENG format

Sometimes both the SI orders of magnitude and the engineering format have been accused of casting doubt on the precision of the values obtained.

In fact, the exponential representation gives the precision of the results in a very simple and clear way, namely by the number of digits after the digit. For example, the results 5 E-4 m, 5.0 E-4 m and 5.00 E-4 m do not mean the same thing. However, these three different results would have to be reduced indiscriminately to 500 µm and 500 E-6 m in both the SI and ENG formats.

This apparent shortcoming of the SI and ENG formats can be overcome by specifying the results as decimal fractions of the higher order of magnitude, i.e. in the above example as 0.5 mm, 0.50 mm and 0.500 mm respectively, or as 0.5 E-3 m, 0.50 E-3 m and 0.500 E-3 m respectively. The indication of precision is restored. In any case, this procedure is only necessary for results that can be determined to no more than two decimal places, a rather rare case in science.