ISO 80000-1-2009 pdf free download.Quantities and units Part 1 :General Grandeurs et unites Partie 1 : Generalites.
6.1 Units and numerical values
If a particular example of a quantity of a given kind is chosen as a reference quantity called the unit (see 3.9), then any other quantity of the same kind can be expressed in terms of this unit, as a product of this unit and a number. That number is called the numerical value of the quantity expressed in this unit.
EXAMPLE 1 The wavelength of one of the sodium spectral lines is 45,896x 10-7m
Here, 2 is the symbol for the quantity wavelength, m is the symbol for the unit of length, the metre, and 5,896 x iO is the numerical value of the wavelength expressed in metres.
In formal treatments of quantities and units, this relation may be expressed in the form
Q = {Q}. [Q]
where Q Is the symbol for the quantity. [Q] is the symbol for the unit and {Q} is the symbol for the numerical value of the quantity Q expressed in the unit [QJ. For vectors and tensors, the components are quantities that can be expressed as described above. Vectors and tensors can also be expressed as a numerical value vector or tensor, respectively, multiplied by a unit.
If a quantity is expressed in another unit that is k times the first unit, the new numerical value becomes Ilk times the first numerical value because the quantity, which is the product of the numerical value and the unit, is independent of the unit.
EXAMPLE 2
Changing the unit for the wavelength in the previous example from the metre to the nanometre, which is 1O times the metre, leads to a numerical value which Is iO the numerical value of the quanhty expressed in metres.
6.4 Coherent systems of units
Units might be chosen arbitrarily, but making an independent choice of the unit for each quantity would lead to the appearance of additional numerical factors in the numerical value equations.
It is possible, however, and in practice more convenient, to choose a system of units in such a way that the numerical value equations have exactly the same form, including the numerical factors, as the corresponding equations in a chosen system of quantities. To establish such a system of units, first one and only one unit for each base quantity is defined. The units of the base quantities are called base units. Then, the units of all derived quantities are expressed in terms of the base units in accordance with the equations in the system of quantities. The units of the derived quantities are called derived units. A system of units defined in this way is called coherent with respect to the system of quantities, including the equations In question.
In a coherent system of units, the expression of each unit corresponds to the dimension of the quantity in question. I.e. the expression of the unit is obtained by replacing the symbols for base dimensions in the quantity dimension by those for the base units. respectively. In particular, a quantity of dimension one acquires the unit one, symbol 1. In such a coherent system of units, no numerical factor other than 1 ever occurs in the expressions for the derived units in terms of the base units.ISO 80000-1-2009 pdf free download.