 TOPICS  # Order of Magnitude

Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities and which are within about a factor of 10 of each other are then said to be "of the same order of magnitude," written .

Hardy and Wright (1979, p. 7) say a real function and positive function with continuous variable that tends to some limit are of the same order of magnitude, written using asymptotic notation as , if for positive constants and independent of . This term is also used for an integer variable that tends to infinity, a real function , and a positive function .

Asymptotic, Asymptotic Notation, Tilde

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## References

Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, 1979.Jeffreys, H. and Jeffreys, B. S. "Orders of Magnitude." §1.08 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 23-24, 1988.

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Order of Magnitude

## Cite this as:

Weisstein, Eric W. "Order of Magnitude." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OrderofMagnitude.html