Order of Magnitude

An Order of Magnitude is the smallest power of ten by which a given number can be represented.

Context:
- A given number, [math]\displaystyle{ N }[/math], can be represented as [math]\displaystyle{ N\times10^m }[/math] or [math]\displaystyle{ N }[/math]E[math]\displaystyle{ m }[/math], where [math]\displaystyle{ m }[/math] is the power of ten.
Example(s):
- The order of magnitude of 2000 is 3 as it can be represented by [math]\displaystyle{ 2\times10^3 }[/math] or 2E3
- 1500 is 2 orders of magnitude larger than 15. The number 1500 can be represented as [math]\displaystyle{ 1.5\times10^3 }[/math] and 15 as [math]\displaystyle{ 1.5\times10 }[/math]
Counter-Example(s):
- Order of a Polynomial.
See: Polynomial Degree, Exponent.

References

(Wikipedia, 2015) ⇒http://wikipedia.org/wiki/Order_of_magnitude
- QUOTE: Orders of magnitude are written in powers of 10. For example, the order of magnitude of 1500 is 3, since 1500 may be written as 1.5 × 10³.

Differences in order of magnitude can be measured on the logarithmic scale in “decades” (i.e., factors of ten).

(Wolfram Mathworld , 1999) ⇒ http://mathworld.wolfram.com/OrderofMagnitude.html
- QUOTE: Physicists and engineers use the phrase “order of magnitude” to refer to the smallest power of ten needed to represent a quantity. Two quantities [math]\displaystyle{ f }[/math] and [math]\displaystyle{ \phi }[/math] which are within about a factor of 10 of each other are then said to be "of the same order of magnitude," written [math]\displaystyle{ f∼\phi }[/math].