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Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...
The Drake equation is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way Galaxy. [1][2][3] The equation was formulated in 1961 by Frank Drake, not for purposes of quantifying the number of civilizations, but as a way to stimulate scientific dialogue at the first ...
If there are 2 oranges and 3 apples, the ratio of oranges to apples is 2:3, and the ratio of oranges to the total number of pieces of fruit is 2:5. These ratios can also be expressed in fraction form: there are 2/3 as many oranges as apples, and 2/5 of the pieces of fruit are oranges.
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
In the expression 6/x vision, the numerator (6) is the distance in metres between the subject and the chart and the denominator (x) the distance at which a person with 6/6 acuity would discern the same optotype. Thus, 6/12 means that a person with 6/6 vision would discern the same optotype from 12 metres away (i.e. at twice the distance).
An interesting feature of ancient Egyptian mathematics is the use of unit fractions. [7] The Egyptians used some special notation for fractions such as 1 / 2 , 1 / 3 and 2 / 3 and in some texts for 3 / 4 , but other fractions were all written as unit fractions of the form 1 / n or sums of such unit ...
Fractions such as 1 ⁄ 3 are displayed as decimal approximations, for example rounded to 0.33333333. Also, some fractions (such as 1 ⁄ 7, which is 0.14285714285714; to 14 significant figures) can be difficult to recognize in decimal form; as a result, many scientific calculators are able to work in vulgar fractions or mixed numbers.
Many variations of the problem have been explored, but most do not lead to a simple closed-form solution. Flexible retirement age can be taken into account. [5] A utility function other than CRRA can be used. Transaction costs can be introduced. For proportional transaction costs the problem was solved by Davis and Norman in 1990. [6]