# Magnitude

## Magnitude

Characteristic or property of a mathematical or physical object that can be measured or calculated and that is often expressed accompanied by a unit of measurement.

• The measure expresses the magnitude of a measurable object in order to make this magnitude comparable to other magnitudes of the same type.
• The concept of magnitude is used in mathematics to refer to concepts associated with various phenomena such as lengths, areas, volumes, masses, angles, speeds, durations, vectors, random or statistical distributions of data, etc.
• Unless a convention explicitly mentions otherwise, a magnitude is always expressed (measured) by a positive number.

### Examples

• The length of a segment is a measurable magnitude that we can express using various units of measurement such as the metre, the centimetre, etc
• The number −100, to express a duration in time starting from a moment chosen as the origin, is subject to this convention: a positive sign expresses a duration of time that has passed after the moment of origin and a negative sign expresses a duration of time that has passed before the origin. This involves the concept of sense.
• From a physical point of view, the temperature of a body is a non-measurable magnitude because the temperature has the effect of modifying certain physical or geometric properties of bodies as well as their states (solid, liquid, gas). Therefore, properly speaking, we cannot use the term to measure to correctly assess a temperature. So, for a given temperature, we must match a number that comes from the measure of another magnitude characterizing a property that also depends on the temperature. This is due to the fact that a non-measurable magnitude is a magnitude for which we cannot find a common benchmark between two evaluations. That’s why, if we recorded a temperature of 5°C outside on Monday, we cannot give meaning to the expression “tomorrow it will be three times colder.
• We cannot carry out arithmetic operations with non-measurable magnitudes.