A rate is a comparison of the change in one quantity, such as distance, temperature, weight, or time, to the change in a second quantity of this type. The comparison is often shown as a formula, a ratio, or a fraction, dividing the change in the first quantity by the change in the second quantity. When the changes being compared occur over a measurable period of time, their ratio determines an average rate of change. When the changes being compared both occur instantaneously, the rate is instantaneous.
One common and very important type of rate is the time rate of change. This type of rate compares the change in one quantity to a simultaneous change in time. Common examples of time rates of change are: birth rates, rates of speed, rates of acceleration, rates of pay, and interest rates. In each case, the rate is determined by dividing the change in a measured quantity (population, location, speed, and earnings, etc.) by the length of a corresponding elapsed time. For instance, distance traveled (change in location) compared to the length of time traveled (change in time) is rate of speed.
In all cases, a rate is specified by two units, one for each of the quantities being compared. For example, speed cannot be expressed in units of distance alone, such as miles or kilometers. It is necessary to say how many units of distance are traveled in a specific period of time, such as miles per hour or kilometers per second. So the units of a rate are also a ratio—a ratio of the units used to measure the two changes being compared.
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