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The minim (abbreviated min, ♏︎ or ♍︎) is a unit of volume in both the imperial and U.S. customary systems of measurement. Specifically, in the imperial system, it is 1 ⁄ 60 of an imperial fluid drachm [1] [2] or 1 ⁄ 480 of an imperial fluid ounce; in the U.S. customary system, it is 1 ⁄ 60 of a US customary fluid dram or 1 ⁄ 480 of a US customary fluid ounce.
A simple fraction (also known as a common fraction or vulgar fraction) [n 1] 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 .
A unit fraction is a positive fraction with one as its numerator, 1/ n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, ...
180 is a 61-gonal number, [2] while 61 is the 18th prime number. Half a circle has 180 degrees, [7] and thus a U-turn is also referred to as a 180. Summing Euler's totient function φ(x) over the first + 24 integers gives 180. In binary it is a digitally balanced number, since its binary representation has the same number of zeros as ones ...
An equivalent definition is sometimes useful: if a and b are integers, then the fraction a / b is irreducible if and only if there is no other equal fraction c / d such that | c | < | a | or | d | < | b |, where | a | means the absolute value of a. [4] (Two fractions a / b and c / d are equal or equivalent if and ...
Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two integers, but it can be represented as a continued fraction. Using calculus, e may also be represented as an infinite series, infinite product, or other types of limit of a sequence.
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
By consequence, we may get, for example, three different values for the fractional part of just one x: let it be −1.3, its fractional part will be 0.7 according to the first definition, 0.3 according to the second definition, and −0.3 according to the third definition, whose result can also be obtained in a straightforward way by