Editing Order of magnitude (section)

==Uses==
Orders of magnitude are used to make approximate comparisons.  If numbers differ by one order of magnitude, ''x'' is ''about'' ten times different in quantity than ''y''.  If values differ by two orders of magnitude, they differ by a factor of about 100. Two numbers of the same order of magnitude have roughly the same scale: the larger value is less than ten times the smaller value.
The growing amounts of Internet data have led to addition of new [[SI prefix]]es over time, most recently in 2022.<ref>{{cite journal
 |url        = https://www.nature.com/articles/d41586-022-03747-9
 |title      = How many yottabytes in a quettabyte? Extreme numbers get new names
 |last       = Gibney 
 |first      = Elizabeth
 |journal = Nature
 |year = 2022
 |doi = 10.1038/d41586-022-03747-9
 |pmid = 36400954
 |s2cid = 253671538
 |access-date = 20 November 2022
}}</ref>

{| class="wikitable"
! In words
! Prefix (Symbol)
! Decimal
! [[Exponent#Powers of ten|Power]]<br />of&nbsp;ten
! Order&nbsp;of<br />magnitude
|-
|nonillionth
|quecto- (q)
| align=right | {{val|0.000000000000000000000000000001}}
| 10<sup>−30</sup>
| −30
|-
|octillionth
|ronto- (r)
| align=right | {{val|0.000000000000000000000000001}}
| 10<sup>−27</sup>
| −27
|-
| septillionth
| yocto- (y)
| align=right | {{val|0.000000000000000000000001}}
| 10<sup>−24</sup>
| −24
|-
| sextillionth
| zepto- (z)
| align=right | {{val|0.000000000000000000001}}
| 10<sup>−21</sup>
| −21
|-
| quintillionth
| atto- (a)
| align=right | {{val|0.000000000000000001}}
| 10<sup>−18</sup>
| −18
|-
| quadrillionth
| femto- (f)
| align=right | {{val|0.000000000000001}}
| 10<sup>−15</sup>
| −15
|-
| trillionth
| pico- (p)
| align=right | {{val|0.000000000001}}
| 10<sup>−12</sup>
| −12
|-
| billionth
| nano- (n)
| align=right | {{val|0.000000001}}
| 10<sup>−9</sup>
| −9
|-
| millionth
| [[micro-]] ([[Mu (letter)|μ]])
| align=right | {{val|0.000001}}
| 10<sup>−6</sup>
| −6
|-
| thousandth
| milli- (m)
| align=right | 0.001
| 10<sup>−3</sup>
| −3
|-
| hundredth
| centi- (c)
| align=right | 0.01
| 10<sup>−2</sup>
| −2
|-
| tenth
| deci- (d)
| align=right | 0.1
| 10<sup>−1</sup>
| −1
|-
| one
| &nbsp;
| align=right | 1
| 10<sup>0</sup>
| 0
|-
| ten
| [[deca-]] (da)
| align=right | 10
| 10<sup>1</sup>
| 1
|-
| hundred
| hecto- (h)
| align=right | 100
| 10<sup>2</sup>
| 2
|-
| thousand
| kilo- (k)
| align=right | {{val|1000|fmt=none}}
| 10<sup>3</sup>
| 3
|-
| million
| mega- (M)
| align=right | {{val|1000000}}
| 10<sup>6</sup>
| 6
|-
| billion
| giga- (G)
| align=right | {{val|1000000000}}
| 10<sup>9</sup>
| 9
|-
| trillion
| tera- (T)
| align=right | {{val|1000000000000}}
| 10<sup>12</sup>
| 12
|-
| quadrillion
| peta- (P)
| align=right | {{val|1000000000000000}}
| 10<sup>15</sup>
| 15
|-
| quintillion
| exa- (E)
| align=right | {{val|1000000000000000000}}
| 10<sup>18</sup>
| 18
|-
| sextillion
| zetta- (Z)
| align=right | {{val|1000000000000000000000}}
| 10<sup>21</sup>
| 21
|-
| septillion
| yotta- (Y)
| align=right | {{val|1000000000000000000000000}}
| 10<sup>24</sup>
| 24
|-
| octillion
| ronna- (R)
| align=right | {{val|1000000000000000000000000000}}
| 10<sup>27</sup>
| 27
|-
| nonillion
| quetta- (Q)
| align=right | {{val|1000000000000000000000000000000}}
| 10<sup>30</sup>
| 30
|-
! In words
! Prefix (Symbol)
! Decimal
! [[Exponent#Powers of ten|Power]]<br />of&nbsp;ten
! Order&nbsp;of<br />magnitude
|}

===Calculating the order of magnitude by truncation===
The order of magnitude of a number is, intuitively speaking, the number of powers of 10 contained in the number.  More precisely, the order of magnitude of a number can be defined in terms of the [[common logarithm]], usually as the [[integer]] part of the logarithm, obtained by [[truncation]].{{contradictory inline|section=Definition|date=November 2023}}  For example, the number {{val|4000000}} has a logarithm (in base 10) of 6.602; its order of magnitude is 6.  When truncating, a number of this order of magnitude is between 10<sup>6</sup> and 10<sup>7</sup>. In a similar example, with the phrase "seven-figure income", the order of magnitude is the number of figures minus one, so it is very easily determined without a calculator to be 6. An order of magnitude is an approximate position on a [[logarithmic scale]].

===Order-of-magnitude estimate===
An order-of-magnitude estimate of a variable, whose precise value is unknown, is an estimate [[Rounding|rounded]] to the nearest power of ten.  For example, an order-of-magnitude estimate for a variable between about 3 billion and 30 billion (such as the human [[population]] of the [[Earth]]) is 10 [[1000000000 (number)|billion]]. To round a number to its nearest order of magnitude, one rounds its logarithm to the nearest integer.  Thus {{val|4000000}}, which has a logarithm (in base 10) of 6.602, has 7 as its nearest order of magnitude, because "nearest" implies rounding rather than truncation.  For a number written in scientific notation, this logarithmic rounding scale requires rounding up to the next power of ten when the multiplier is greater than the square root of ten (about 3.162). For example, the nearest order of magnitude for {{val|1.7|e=8}} is 8, whereas the nearest order of magnitude for {{val|3.7|e=8}} is 9. An order-of-magnitude estimate is sometimes also called a [[zeroth order approximation]].