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A percentage change is a way to express a change in a variable. It represents the relative change between the old value and the new one. [6]For example, if a house is worth $100,000 today and the year after its value goes up to $110,000, the percentage change of its value can be expressed as = = %.
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
If the initial amount p leads to a percent change x, and the second percent change is y, then the final amount is p (1 + 0.01 x)(1 + 0.01 y). To change the above example, after an increase of x = 10 percent and decrease of y = −5 percent, the final amount, $209, is 4.5% more than the initial amount of $200.
It is thus the ratio of the relative (percentage) change in the function's output () with respect to the relative change in its input , for infinitesimal changes from a point (, ()). Equivalently, it is the ratio of the infinitesimal change of the logarithm of a function with respect to the infinitesimal change of the logarithm of the argument.
The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in the title of his main treatise. [31] [32] Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified ...
As an example, suppose that 30% of widgets made in a factory are defective. Six months later, 20% of widgets are defective. The percentage change is 20% − 30% / 30% = − 1 / 3 = −33 + 1 / 3 %, while the percentage point change is −10 percentage points.
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