Scientific notation (standard index notation) is a concise way of recording numbers by integer powerss of ten, that is used to record numbers which are notably large or small. Such notation is used to record physical quantities without including trailing, or leading, zeros.
- 101 = 10
- 102 = 100
- 103 = 1000
- 106 = 1,000,000
- 109 = 1,000,000,000
- 1020 = 100,000,000,000,000,000,000
- 10-1 = 1/10 = 0.1
- 10-3 = 1/1000 = 0.001
- 10-9 = 1/1,000,000,000 = 0.000000001
Scientific notation is highly useful for quoting physical quantities, as they can only be measured to within certain error limits and so quoting just the digits that are certain (the "significant digits") gives all the information required without wasting space.
If a physical quantity is quoted using scientific notation, it is usually assumed to be accurate to the quoted number of digits of precision - for instance if a figure 1.2340 × 106 metres is quoted, the actual figure is assumed to be between 1,233,950 metres as a lower bound and 1,234,050 metres as an upper bound. However, where precision in such measurements is crucial, much more sophisticated expressions of measurement error must be used.
Scientific notation also avoids regional differences to certain quantifiers, notably "billion", where if scientific notation is used, the quantity is always known.
See also: Orders of magnitude, floating point.