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Thus the fraction 3 / 4 can be used to represent the ratio 3:4 (the ratio of the part to the whole), and the division 3 ÷ 4 (three divided by four). We can also write negative fractions, which represent the opposite of a positive fraction. For example, if 1 / 2 represents a half-dollar profit, then − 1 / 2 represents ...
If the ratio consists of only two values, it can be represented as a fraction, in particular as a decimal fraction. For example, older televisions have a 4:3 aspect ratio, which means that the width is 4/3 of the height (this can also be expressed as 1.33:1 or just 1.33 rounded to two decimal places). More recent widescreen TVs have a 16:9 ...
Another meaning for generalized continued fraction is a generalization to higher dimensions. For example, there is a close relationship between the simple continued fraction in canonical form for the irrational real number α, and the way lattice points in two dimensions lie to either side of the line y = αx. Generalizing this idea, one might ...
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]
For instance, as Wagon discovered, [4] the odd greedy expansion for 3/179 has 19 terms, the largest of which is approximately 1.415×10 439491. Curiously, the numerators of the fractions to be expanded in each step of the algorithm form a sequence of consecutive integers:
Those reciprocals of primes can be associated with several sequences of repeating decimals. For example, the multiples of 1 / 13 can be divided into two sets, with different repetends. The first set is: 1 / 13 = 0. 076923 10 / 13 = 0. 769230 9 / 13 = 0. 692307 12 / 13 = 0. 923076 3 / 13 = 0 ...
While virtually all real numbers k will eventually have infinitely many convergents m / n whose distance from k is significantly smaller than this limit, the convergents for φ (i.e., the numbers 5 / 3 , 8 / 5 , 13 / 8 , 21 / 13 , etc.) consistently "toe the boundary", keeping a distance of almost exactly ...
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...