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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 ...
9.287 = 18.574 / 2 = 2.51 × 3.7. The additional equivalent forms above assume that the constants 3.7 and 2.51 in the formula at the top of this section are exact.
How much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, an alternative form of the ideal gas law may be useful. The chemical amount, n (in moles), is equal to total mass of the gas (m) (in kilograms) divided by the molar mass, M (in kilograms per mole): =.
The first four hyperoperations are shown here, with tetration being considered the fourth in the series. The unary operation succession, defined as ′ = +, is considered to be the zeroth operation.
Castigliano's method for calculating displacements is an application of his second theorem, which states: If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Q i then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement q i in the direction of Q i.
u+00be ¾ vulgar fraction three quarters The "one-half" symbol has its own code point as a precomposed character in the Latin-1 Supplement block of Unicode , rendering as ½ . The reduced size of this symbol may make it illegible to readers with relatively mild visual impairment ; consequently the decomposed forms 1 ⁄ 2 or 1 / 2 may ...
During the early modern period, mathematics began to develop at an accelerating pace in Western Europe, with innovations that revolutionized mathematics, such as the introduction of variables and symbolic notation by François Viète (1540–1603), the introduction of logarithms by John Napier in 1614, which greatly simplified numerical ...
About 68% of values drawn from a normal distribution are within one standard deviation σ from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. [8] This fact is known as the 68–95–99.7 (empirical) rule, or the 3-sigma rule.