# Order of Magnitude

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

**AKA:**OOM.**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.
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**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]
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**Counter-Example(s):****See:**Polynomial Degree, Exponent, Orders of Magnitude (Numbers), Logarithm, Logarithmic Distribution, Binary_number, Difference (Mathematics), Measured, Logarithmic Scale, Decade (Log Scale).

## References

### 2024

- (Wikipedia, 2024) ⇒ https://en.wikipedia.org/wiki/Order_of_magnitude Retrieved:2024-6-5.
- 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 base of the logarithm and the representative of values of magnitude one. Logarithmic distributions 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 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 format, the magnitude can be understood in terms of the amount of computer memory needed to store that value.Differences in order of magnitude can be measured on a base-10 logarithmic scale in "decades" (i.e., factors o

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### 2015

- (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 × 10^{3}**.**

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

### 1999

- (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].