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'''Order of magnitude''' is a classifying scale used to compare the relative size or quantity of values. It is typically based on powers of ten, where each order of magnitude is ten times larger or smaller than the one before it. This concept is widely used in various fields such as [[physics]], [[chemistry]], [[engineering]], and [[economics]] to simplify the comparison of vastly different quantities.

==Definition==
An order of magnitude is a way to express the approximate size of a number in terms of powers of ten. For example, the number 1,000 is three orders of magnitude larger than the number 1, because 1,000 = 10^3. Similarly, 0.01 is two orders of magnitude smaller than 1, because 0.01 = 10^-2.

==Applications==
===Science===
In [[science]], orders of magnitude are used to compare quantities such as [[mass]], [[length]], and [[time]]. For instance, the mass of the [[Earth]] is about 10^24 kilograms, while the mass of a [[proton]] is about 10^-27 kilograms. This shows that the Earth is 51 orders of magnitude more massive than a proton.

===Engineering===
In [[engineering]], orders of magnitude help in understanding the scale of different phenomena. For example, the [[Richter scale]] for measuring the magnitude of [[earthquakes]] is logarithmic, meaning each whole number increase on the scale represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release.

===Economics===
In [[economics]], orders of magnitude can be used to compare the size of economies, budgets, or financial transactions. For example, the [[gross domestic product]] (GDP) of a small country might be on the order of 10^9 dollars, while the GDP of a large country could be on the order of 10^12 dollars.

==Examples==
* The [[speed of light]] is approximately 3 x 10^8 meters per second.
* The [[age of the universe]] is estimated to be around 13.8 billion years, or 1.38 x 10^10 years.
* The [[diameter of a hydrogen atom]] is about 10^-10 meters.

==Related Concepts==
* [[Logarithm]]
* [[Scientific notation]]
* [[Scale (ratio)]]
* [[Magnitude (mathematics)]]

==See Also==
* [[Orders of magnitude (length)]]
* [[Orders of magnitude (mass)]]
* [[Orders of magnitude (time)]]
* [[Orders of magnitude (data)]]

==References==
{{Reflist}}

==External Links==
{{Commons category|Orders of magnitude}}

[[Category:Mathematics]]
[[Category:Measurement]]
[[Category:Scientific concepts]]

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Order of magnitude - Revision history

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