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dimensionless number

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Pi is an example of a dimensionless number. A dimensionless number doesn’t imply any measurement units. Pi is just 3.14, not 3.14 miles nor pounds nor cents. In contrast, c, the speed of light, must be stated in terms of miles per second or meters per second or other equivalent measurement units. The symbol c is not a dimensionless number.

Many dimensionless numbers are constants, like pi and e (2.718…). But many dimensionless numbers are not constants, for example, decibels (sound level) and pH (degree of acidity). The pH level can range from 0 to 14. We don’t say a “pH of 3 volts” or “3 dollars.” We just say that the pH is 3, period.

Dimensionless numbers are also called “dimensionless quantities,” “quantities of dimension one,” “bare numbers,” and “bare quantities.”

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