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Order of magnitude is a concept used to discuss the scale of numbers in relation to one another. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are within about a factor of 10 of each other. [1] For example, 1 and 1.02 are within an order of magnitude.
Scale analysis (or order-of-magnitude analysis) is a powerful tool used in the mathematical sciences for the simplification of equations with many terms. First the approximate magnitude of individual terms in the equations is determined. Then some negligibly small terms may be ignored.
For example, an audio amplifier will usually have a frequency band ranging from 20 Hz to 20 kHz and representing the entire band using a decade log scale is very convenient. Typically the graph for such a representation would begin at 1 Hz (10 0 ) and go up to perhaps 100 kHz (10 5 ), to comfortably include the full audio band in a standard ...
The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages. It is summarized as: [2] [5] Parentheses; Exponentiation; Multiplication and division; Addition and subtraction
Thus the "order of magnitude" of a number (on a larger scale than usually meant), can be characterized by the number of times (n) one has to take the to get a number between 1 and 10. Thus, the number is between 10 ↑ ↑ n {\displaystyle 10\uparrow \uparrow n} and 10 ↑ ↑ ( n + 1 ) {\displaystyle 10\uparrow \uparrow (n+1)} .
The kilogram is the only standard unit to include an SI prefix (kilo-) as part of its name. The gram (10 −3 kg) is an SI derived unit of mass. However, the names of all SI mass units are based on gram, rather than on kilogram; thus 10 3 kg is a megagram (10 6 g), not a *kilokilogram.
Thus one will expect to be within 1 ⁄ 8 to 8 times the correct value – within an order of magnitude, and much less than the worst case of erring by a factor of 2 9 = 512 (about 2.71 orders of magnitude). If one has a shorter chain or estimates more accurately, the overall estimate will be correspondingly better.
This template calculates the order of magnitude of numbers within the ranges 10^300 to 10^−300 and −10^−300 to −10^300. Template parameters [Edit template data] Parameter Description Type Status Number 1 The number to find the order of magnitude of Number required See also {{ Orders of magnitude }} {{ Fractions }} {{ Fractions and ratios }} The above documentation is transcluded from ...