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1/52! chance of a specific shuffle Mathematics: The chances of shuffling a standard 52-card deck in any specific order is around 1.24 × 10 −68 (or exactly 1 ⁄ 52!) [4] Computing: The number 1.4 × 10 −45 is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.
The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. Until the mid-1920s, the unit for loss was miles of standard cable (MSC). 1 MSC corresponded to the loss of power over one mile (approximately 1.6 km) of standard telephone cable at a frequency of 5000 radians per second (795.8 Hz), and matched closely the smallest attenuation detectable to a ...
For example, among the positive integers of at most 1000 digits, about one in 2300 is prime (log(10 1000) ≈ 2302.6), whereas among positive integers of at most 2000 digits, about one in 4600 is prime (log(10 2000) ≈ 4605.2). In other words, the average gap between consecutive prime numbers among the first N integers is roughly log(N). [3]
In chemistry the negative of the decimal logarithm, the decimal cologarithm, is indicated by the letter p. [63] For instance, pH is the decimal cologarithm of the activity of hydronium ions (the form hydrogen ions H + take in water). [64] The activity of hydronium ions in neutral water is 10 −7 mol·L −1, hence a pH of 7. Vinegar typically ...
The fine-structure constant gives the maximum positive charge of an atomic nucleus that will allow a stable electron-orbit around it within the Bohr model (element feynmanium). [20] For an electron orbiting an atomic nucleus with atomic number Z the relation is mv 2 / r = 1 / 4πε 0 Ze 2 / r 2 .
The variance of X is a k×k symmetric positive-definite matrix V. The multivariate normal distribution is a special case of the elliptical distributions . As such, its iso-density loci in the k = 2 case are ellipses and in the case of arbitrary k are ellipsoids .
Of particular note is the use in Chinese mathematics of a decimal positional notation system, the so-called "rod numerals" in which distinct ciphers were used for numbers between 1 and 10, and additional ciphers for powers of ten. [108]
2000 BC: Multiplication tables in a base-60, rather than base-10 (decimal), system from Babylon. [7] 2000 BC: Primitive positional notation for numerals is seen in the Babylonian cuneiform numerals. [8] However, the lack of clarity around the notion of zero made their system highly ambiguous (e.g. 13 200 would be written the same as 132). [9]