Editing Order of magnitude (section)

==Non-decimal orders of magnitude==
{{See also|Logarithmic scale}}
An order of magnitude is an approximation of the [[logarithm]] of a value relative to some contextually understood reference value, usually 10, interpreted as the [[Radix|base]] of the logarithm and the representative of values of magnitude one. [[Logarithmic distribution]]s are common in nature and considering the order of magnitude of values sampled from such a distribution can be more intuitive. When the reference value is 10, the order of magnitude can be understood as the number of digits minus one in the base-10 representation of the value. Similarly, if the reference value is one of some powers of 2 since computers store data in a [[Binary_number|binary]] format, the magnitude can be understood in terms of the amount of computer memory needed to store that value.

===Irrational orders of magnitude===
Other orders of magnitude may be calculated using bases other than integers. In the field of [[astronomy]], the nighttime brightnesses of celestial bodies are ranked by [[Magnitude (astronomy)|"magnitudes"]] in which each increasing level is brighter by a [[factor (arithmetic)|factor]] of <math>\sqrt[5]{100} \approx 2.512</math> greater than the previous level. Thus, a level being 5 magnitudes brighter than another indicates that it is a factor of <math>(\sqrt[5]{100})^5 = 100</math> times brighter: that is, two base 10 orders of magnitude. 

This series of magnitudes forms a logarithmic scale with a base of <math>\sqrt[5]{100}</math>.

===Base 1,000,000 orders of magnitude===
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 {{val|1000000}}. It can be seen that the order of magnitude is included in the number name in this example, because bi- means 2, tri- means 3, etc. (these make sense in the long scale only), and the suffix -illion tells that the base is {{val|1000000}}. But the number names billion, trillion themselves (here with [[Long and short scales|other meaning]] than in the first chapter) are not names of the ''orders of'' magnitudes, they are names of "magnitudes", that is the ''numbers'' {{val|1000000000000}} etc.

{| class="wikitable"
! Order of magnitude !! Is [[Common logarithm|log<sub>10</sub>]] of !! Is log<sub>{{val|1000000}}</sub> of !! Short scale !! Long scale
|-
| 1 || align=right |   {{val|10}}          || align=right |             {{val|1000000}} || align=right |     million || align=right |  million
|-
| 2 || align=right |  {{val|100}}          || align=right |       {{val|1000000000000}} || align=right |    trillion || align=right |  billion
|-
| 3 || align=right | {{val|1000|fmt=none}} || align=right | {{val|1000000000000000000}} || align=right | quintillion || align=right | trillion
|-
| 4 || align=right | {{val|10000|fmt=none}} || align=right | (1 000 000)<sup>4</sup> || align=right | septillion || align=right | quadrillion
|-
| 5 || align=right | {{val|100000|fmt=none}} || align=right | (1 000 000)<sup>5</sup> || align=right | nonillion || align=right | quintillion
|}

[[SI]] units in the table at right are used together with [[SI prefix]]es, which were devised with mainly base 1000 magnitudes in mind. [[Binary prefix#IEC standard prefixes|The IEC standard prefixes]] with base 1024 were invented for use in electronic technology.