Scientific quantities

A scientific quantity is a quantifiable or assignable property ascribed to a scientific system or process –i.e., a system or process belonging to the scope of science–. The value of this property can be expressed as the product of a mathematical quantity and a reference or unit.

The term quantity derives from the Latin quantus meaning how much. Examples of scientific quantities are the length of a pencil, the mass of the moon, the electric charge of the electron, the half-life of the production of virus by infected cells, the temperature of a flame, the chemical composition of a sample of water, and the volumic mass –mass density– of a Escherichia Coli.

Formally, the value of a quantity \( Q \) can be expressed as 1

\[ Q = \{Q\} [Q] \; . \]

Here \( \{Q\} \) is the number of times that the unit \( [Q] \) is contained in the value of the quantity. For example \( T = 298 \;\mathrm{K} \) is temperature in Kelvins, whereas \( h = 46 \;\mathrm{m} \) is height in metres. In this way, the equations and inequalities used in science hold for any units –units are a matter of human choice and no law in nature should depend on them–.

The reference \( [Q] \) can be arbitrary, but for the purpose of safe and efficient communication with the rest of members of the scientific and related communities, a set of units are defined and adopted by convenience 2. The more relevant of them is the International System of Units (SI) 1.

Two kinds of mathematical quantities \( \{Q\} \) are encountered in scientific quantities: exact and inexact. Exact mathematical quantities are known exactly. For example, there are exactly \( 12 \) eggs in a dozen, the speed of light –in metres per second– is exactly \( 299 792 458 \) in the SI. Inexact mathematical quantities are those having some uncertainty arising from measurements. Confidence intervals are a way to express the uncertainty of a measurement.

We prefer the term scientific quantity over the old term physical quantity, because chemical and biological quantities also exist in science. This reinforces a unified vision of science. The word physical in physical quantity often means quantitative –see its usage by NIST 3–, but it is also used as meaning belong to physics.

Contrary to the definitions given by NIST, BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML 1,4, the value of a quantity is not the product of a number and a unit, because for inexact quantities, \( \{Q\} \) is given by an interval. Some textbooks take an opposite viewpoint and state that No physical quantity can be determined with complete accuracy because our senses are physically limited, even when extended with microscopes, cyclotrons, and other instruments. 5. This is also incorrect because, as shown above, we know some quantities exactly.