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1Relating to or expressed as a numerical value that is not a whole number, especially a fraction less than one.
‘It is natural to think that the behavior of iterations that start with z 0 = e it, where t is not a fractional part of 2 is chaotic and generate the set dense on the circle.’
‘The part after the decimal point in number r is often called the fractional part of r and written as frac (r).’
‘One of the first topics he studied, which developed from his early work on electromagnetism, was a new topic, now called the fractional calculus.’
‘There the author describes how mathematicians moved from studying first derivatives, second derivatives, etc., to study fractional derivatives.’
‘Much of Burnside's work on hydrodynamics involved the use of complex variable and in papers of 1891 and 1892 he considered the group of linear fractional transformations of a complex variable.’
‘Note that sometimes a new point will be plotted further to the right than any previous one (i.e. its fractional part will be larger than any before it).’
‘The second algorithm involves linear programming with randomized rounding to convert fractional assignments into integral ones.’
‘Each time we take the reciprocal of the fractional part we usually get another long list of decimal places.’
‘However, the Babylonians has no notation to indicate where the integer part ended and the fractional part began.’
‘Both have identical fractional parts after the decimal point.’
‘Many techniques are available to better assess the true relationship between a continuous predictor and an outcome variable, including fractional polynomials, smoothing splines or other smoothing functions.’
‘There are sections of the book devoted to arithmetic and geometric progressions, including progressions with a fractional numbers of terms, and formulas for the sum of certain finite series are given.’
‘He also studied fractional numbers and learnt much of the impressive contributions that the Arabs had made to mathematics over the preceding 400 years.’
‘In the fractional method shown on this page, we're adding fractional completions in a single unit of time; whereas when we began, we were adding whole completions in multiple units of time.’
‘He also worked on asymptotic analysis, fractional integration and singular partial differential equations.’
‘The computer programs implement basic mathematical principles such as basic geometry and fractional math.’
‘Any fractional or decimal value must be multiplied by a whole number to eliminate fractional subscripts.’
‘This number could be either integral or fractional.’
‘Bosanquet's early 1930s papers were on series and integration, a 1930 paper being on fractional integration, a topic he would return to many times.’
‘He examined series expansions and looked at series with fractional powers.’
1.1Small or tiny in amount.
‘there was a fractional hesitation before he said yes’
‘Unemployment figures showed a fractional improvement but separate statistics on redundancies showed an increase of about one-third on this time last year.’
‘The researchers found that their bimetallic cathodes worked even more effectively in the ORR than platinum alone, despite only containing a fractional amount of platinum in the monolayer.’
‘Astronomers often express the amount of redshift, the fractional change of wavelength, as a dimensionless number, z.’
‘Infants are very sensitive to it and only the most infinitesimal fractional doses should be used.’
‘Anticipating the beat by fractional amounts on single chords or notes (Blues singers do this all the time to express pain and suffering).’
‘Since, for example, a proton has a charge of + 1, a quark would have a fractional charge.’
‘Tiny though this fractional increase seems when expressed this way, the overall amounts are huge.’
‘And my input is a tiny, fractional thing of a film, and how it's dealt with in post-production, how the studio is marketed.’
1.2Chemistry Relating to or denoting the separation of components of a mixture by making use of their differing physical properties.
‘fractional crystallization’
‘Very few of the components come out of the fractional distillation column ready for market.’
‘Distillation can be used to separate volatile liquids by a process known as fractional distillation.’