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In mathematics, a rate is a ratio between two measurements with different units.^{[1]} If the unit or quantity in respect of which something is changing is not specified, usually the rate is per unit time. However, a rate of change can be specified per unit time, or per unit of length or mass or another quantity. The most common type of rate is "per unit time", such as speed, heart rate and flux. Ratios that have a non-time denominator include exchange rates, literacy rates and electric flux.
In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate is expressed "beats per minute"). A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%) or fraction or as a multiple.
Often rate is a synonym of rhythm or frequency, a count per second (i.e., Hertz); e.g., radio frequencies or heart rate or sample rate.
A rate of change can be formally defined in two ways:^{[2]}
where f(x) is the function with respect to x over the interval from a to a+h. An instantaneous rate of change is equivalent to a derivative.
An example to contrast the differences between the average and instantaneous definitions: the speed of a car can be calculated:
In chemistry and physics:
In computing:
In finance:
Miscellaneous definitions:
Time, Energy, Velocity, Kinematics, Mass
Energy, Time, Classical mechanics, Force, Acceleration
Research, Speed, Collision, Graphical representation, Average
Data, Database, Insurance, Legislation, U.s.