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### order of magnitude

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order of magnitude
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{{short description|Scale of numbers with a fixed ratio}}(File:Orders of magnitude (english annotations).png|thumb|The scale of everything. It begins with spacetime (quantum foam) and moves through small elementary particles, intermediate elementary particles, large elementary particles, components of composite particles, the components of atoms, electromagnetic waves, simple atoms, complex atoms, molecules, small viruses, large viruses, chromosomes, cells, hairs, body parts, species, groups of species, small areas such as craters, large areas such as land masses, planets, orbits, stars, small planetary systems, intermediate planetary systems, large planetary systems, collections of stars, star clusters, galaxies, galaxy groups, galaxy clusters, galaxy superclusters, the cosmic web, Hubble volumes, and ends with the Universe.)An order of magnitude is an approximate measure of the number of digits that a number has in the commonly-used base-ten number system. It is equal to the whole number floor of logarithm (base 10). For example, the order of magnitude of 1500 is 3, because 1500 = 1.5 Ã— 103.Differences in order of magnitude can be measured on a base-10 logarithmic scale in â€œdecadesâ€ (i.e., factors of ten).WEB
, Orders of Magnitude
, Brians
, Paus
, 9 May 2013
, Examples of numbers of different magnitudes can be found at Orders of magnitude (numbers).

## Definition

Generally, the order of magnitude of a number is the smallest power of 10 used to represent that number.WEB, Order of Magnitude,weblink Wolfram MathWorld, 3 January 2017, Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity., To work out the order of magnitude of a number N, the number is first expressed in the following form:
N =atimes10^b
where frac{sqrt{10}}{10}leq a

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