Quantities and Units
Physical quantities can be grouped into mutually comparable categories. For example, length, width, diameter and wavelength are all in the same category, that is they are all quantities of the same kind. One particular example of such a quantity can be chosen as a reference quantity, called the unit, and then all other quantities in the same category can be expressed in terms of this unit, multiplied by a number called the numerical value. For example, if we write
- the wavelength is λ = 6.982 × 10−7 m
then "λ" is the symbol for the physical quantity (wavelength), "m" is the symbol for the unit (metre), and "6.982 × 10−7" is the numerical value of the wavelength in metres.
More generally, we can write
- A = {A} ·
where A is the symbol for the quantity, {A} symbolizes the numerical value of A, and represents the corresponding unit in which A is expressed here. Both the numerical value and the unit symbol are factors, and their product is the quantity. A quantity itself has no inherent particular numerical value or unit; as with any product, there are many different combinations of numerical value and unit that lead to the same quantity (e.g., A = 300 · m = 0.3 · km = ...). This ambiguity makes the {A} and notations useless, unless they are used together.
The value of a quantity is independent of the unit chosen to represent it. It must be distinguished from the numerical value of the quantity that occurs when the quantity is expressed in a particular unit. The above curly-bracket notation could be extended with a unit-symbol index to clarify this dependency, as in {λ}m = 6.982 × 10−7 or equivalently {λ}nm = 698.2. In practice, where it is necessary to refer to the numerical value of a quantity expressed in a particular unit, it is notationally more convenient to simply divide the quantity through that unit, as in
- λ/m = 6.982 × 10−7
or equivalently
- λ/nm = 698.2.
This is a particularly useful and widely used notation for labelling the axes of graphs or for the headings of table columns, where repeating the unit after each numerical value can be typographically inconvenient.
Read more about this topic: ISO 31-0
Famous quotes containing the words quantities and/or units:
“James Brown and Frank Sinatra are two different quantities in the universe. They represent two different experiences of the world.”
—Imamu Amiri Baraka [Everett Leroi Jones] (b. 1934)
“Even in harmonious families there is this double life: the group life, which is the one we can observe in our neighbour’s household, and, underneath, another—secret and passionate and intense—which is the real life that stamps the faces and gives character to the voices of our friends. Always in his mind each member of these social units is escaping, running away, trying to break the net which circumstances and his own affections have woven about him.”
—Willa Cather (1873–1947)