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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. The period of the fraction 2 / 7 is ...
Lighting and reflection calculations, as in the video game OpenArena, use the fast inverse square root code to compute angles of incidence and reflection.. Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates , the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
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.
A general development of solutions of Pell's equation = in terms of continued fractions of can be presented, as the solutions x and y are approximates to the square root of n and thus are a special case of continued fraction approximations for quadratic irrationals. [16]
The Sulba Sutras give methods for constructing a circle with approximately the same area as a given square, which imply several different approximations of the value of π. [129] [130] [a] In addition, they compute the square root of 2 to several decimal places, list Pythagorean triples, and give a statement of the Pythagorean theorem. [130]
In academic literature, when inline fractions are combined with implied multiplication without explicit parentheses, the multiplication is conventionally interpreted as having higher precedence than division, so that e.g. 1 / 2n is interpreted to mean 1 / (2 · n) rather than (1 / 2) · n.
Common aspect ratios used in film and display images. The common film aspect ratios used in cinemas are 1.85:1 and 2.40:1. [1] Two common videographic aspect ratios are 4:3 (1. 3:1), [a] the universal video format of the 20th century, and 16:9 (1. 7:1), universal for high-definition television and European digital television.