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Like whole numbers, fractions obey the commutative, associative, and distributive laws, and the rule against division by zero. Mixed-number arithmetic can be performed either by converting each mixed number to an improper fraction, or by treating each as a sum of integer and fractional parts.
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 ...
In chemistry, the mass fraction of a substance within a mixture is the ratio (alternatively denoted ) of the mass of that substance to the total mass of the mixture. [ 1] Expressed as a formula, the mass fraction is: Because the individual masses of the ingredients of a mixture sum to , their mass fractions sum to unity:
Repeating decimal. A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be ...
Mole fraction is numerically identical to the number fraction, which is defined as the number of particles of a constituent N i divided by the total number of all molecules N tot. Whereas mole fraction is a ratio of amounts to amounts (in units of moles per moles), molar concentration is a quotient of amount to volume (in units of moles per litre).
In atmospheric chemistry, mixing ratio usually refers to the mole ratio ri, which is defined as the amount of a constituent ni divided by the total amount of all other constituents in a mixture: The mole ratio is also called amount ratio. [ 2] If ni is much smaller than ntot (which is the case for atmospheric trace constituents), the mole ratio ...
In chemistry and fluid mechanics, the volume fraction is defined as the volume of a constituent Vi divided by the volume of all constituents of the mixture V prior to mixing: [ 1] Being dimensionless, its unit is 1; it is expressed as a number, e.g., 0.18. It is the same concept as volume percent (vol%) except that the latter is expressed with ...
Partial fraction decomposition. 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 ...
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