Scientific notation Guide, Meaning , Facts, Information and Description
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 useful for describing physical quantities, as they can only be measured within certain error limits, and so giving just the digits that are known to be correct (the "significant digits") conveys the information that can safely be used.
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, more sophisticated expressions of measurement error must be used.
Scientific notation also avoids regional differences in certain quantifiers, such as "billion", where the use of scientific notation avoids misunderstanding.