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An order-of-magnitude estimate of a variable, whose precise value is unknown, is an estimate rounded to the nearest power of ten. For example, an order-of-magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion. To round a number to its nearest order of magnitude, one ...
An example is Enrico Fermi's estimate of the strength of the atomic bomb that detonated at the Trinity test, based on the distance traveled by pieces of paper he dropped from his hand during the blast. Fermi's estimate of 10 kilotons of TNT was well within an order of magnitude of the now-accepted value of 21 kilotons. [1] [2] [3]
In the above example, the left-hand side could be of equal order of magnitude as the right-hand side. Rule3-If in the sum of two terms given by = + the order of magnitude of one term is greater than order of magnitude of the other term > ()
A second example of the distribution arises in the case of random complex numbers whose real and imaginary components are independently and identically distributed Gaussian with equal variance and zero mean. In that case, the absolute value of the complex number is Rayleigh-distributed.
This is an accepted version of this page This is the latest accepted revision, reviewed on 17 January 2025. Observation that in many real-life datasets, the leading digit is likely to be small For the unrelated adage, see Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of ...
The template gives 0 for 0. Although, strictly speaking, this is mathematically incorrect it has been designed this way so as to be more useful in other templates. An important example of this is that when used by {} 0 °C or 0 °F is considered to be on the same order of magnitude as ±1 °C or ±1 °F respectively.
The number of alignments found is very sensitive to the allowed width w, increasing approximately proportionately to w k−2, where k is the number of points in an alignment. The following is a very approximate order-of-magnitude estimate of the likelihood of alignments, assuming a plane covered with uniformly distributed "significant" points.
Another example is Victor Weisskopf's pamphlet Modern Physics from an Elementary Point of View. [8] In these notes Weisskopf used back-of-the-envelope calculations to calculate the size of a hydrogen atom, a star, and a mountain, all using elementary physics.