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One half is a rational number that lies midway between nil and unity (which are the elementary additive and multiplicative identities) as the quotient of the first two non-zero integers, . It has two different decimal representations in base ten, the familiar and the recurring , with a similar pair of expansions in any even base; while in odd ...
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 ...
In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions : The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it is a ...
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.
t. e. The number π ( / paɪ /; spelled out as " pi ") is a mathematical constant that is the ratio of a circle 's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics.
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if. φ. where the Greek letter phi ( or ) denotes the golden ratio.
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 (e.g., ). The set of all rational numbers, also referred to as " the rationals ", [2] the field of rationals [3] or the field of ...
Conversely the period of the repeating decimal of a fraction c / d will be (at most) the smallest number n such that 10 n − 1 is divisible by d. For example, the fraction 2 / 7 has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857.