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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 .
For example, a ratio of 3:2 is the same as 12:8. It is usual either to reduce terms to the lowest common denominator, or to express them in parts per hundred . If a mixture contains substances A, B, C and D in the ratio 5:9:4:2 then there are 5 parts of A for every 9 parts of B, 4 parts of C and 2 parts of D.
The decimal expansion of the golden ratio [1] has been calculated to an accuracy of ten trillion (=) digits. [ 66 ] In the complex plane , the fifth roots of unity z = e 2 π k i / 5 {\displaystyle z=e^{2\pi ki/5}} (for an integer k {\textstyle k} ) satisfying z 5 = 1 {\displaystyle z^{5}=1} are the vertices of a pentagon.
Irreducible fraction. An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). [1] In other words, a fraction a b is irreducible if and only if a and ...
The decimal numeral system (also called the base-ten positional numeral system and denary / ˈdiːnəri / [1] or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (decimal fractions) of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is ...
t. e. In computing, floating-point arithmetic (FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. [1]: 3 [2]: 10 For example, 12.345 is a floating-point number in base ten ...
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p and a non-zero denominator q. [1] For example, is a rational number, as is every integer (for example, ). The set of all rational numbers, also referred to as " the rationals ", [2] the field of ...
The real numbers can be constructed as a completion of the rational numbers, in such a way that a sequence defined by a decimal or binary expansion like (3; 3.1; 3.14; 3.141; 3.1415; ...) converges to a unique real number—in this case π. For details and other constructions of real numbers, see Construction of the real numbers.