Non-decimal Orders of Magnitude
See also: Logarithmic scaleOther orders of magnitude may be calculated using bases other than 10. The ancient Greeks ranked the nighttime brightness of celestial bodies by 6 levels in which each level was the fifth root of one hundred (about 2.512) as bright as the nearest weaker level of brightness, so that the brightest level is 5 orders of magnitude brighter than the weakest, which can also be stated as a factor of 100 times brighter.
The different decimal numeral systems of the world use a larger base to better envision the size of the number, and have created names for the powers of this larger base. The table shows what number the order of magnitude aim at for base 10 and for base 1,000,000. It can be seen that the order of magnitude is included in the number name in this example, because bi- means 2 and tri- means 3 (these make sense in the long scale only), and the suffix -illion tells that the base is 1,000,000. But the number names billion, trillion themselves (here with other meaning than in the first chapter) are not names of the orders of magnitudes, they are names of "magnitudes", that is the numbers 1,000,000,000,000 etc.
| order of magnitude | is log10 of | is log1000000 of | short scale | long scale |
|---|---|---|---|---|
| 1 | 10 | 1,000,000 | million | million |
| 2 | 100 | 1,000,000,000,000 | trillion | billion |
| 3 | 1000 | 1,000,000,000,000,000,000 | quintillion | trillion |
SI units in the table at right are used together with SI prefixes, which were devised with mainly base 1000 magnitudes in mind. The IEC standard prefixes with base 1024 were invented for use in electronic technology.
The ancient apparent magnitudes for the brightness of stars uses the base and is reversed. The modernized version has however turned into a logarithmic scale with non-integer values.
Read more about this topic: Order Of Magnitude
Famous quotes containing the words orders and/or magnitude:
“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Constancy has nothing virtuous in itself, independently of the pleasure it confers, and partakes of the temporizing spirit of vice in proportion as it endures tamely moral defects of magnitude in the object of its indiscreet choice.”
—Percy Bysshe Shelley (1792–1822)