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1 km 2 means one square kilometre, or the area of a square of 1000 m by 1000 m. In other words, an area of 1 000 000 square metres and not 1000 square metres. 2 Mm 3 means two cubic megametres, or the volume of two cubes of 1 000 000 m by 1 000 000 m by 1 000 000 m, i.e. 2 × 10 18 m 3, and not 2 000 000 cubic metres (2 × 10 6 m 3).
A mole of a substance has a mass that is its molecular mass expressed in units of grams. The mass of a mole of carbon is 12.0 g, and the mass of a mole of table salt is 58.4 g. The mass of a mole of carbon is 12.0 g, and the mass of a mole of table salt is 58.4 g.
The definition of velocity above satisfies this requirement since it implies that v 1 /v 2 = (d 1 /d 2)/(t 1 /t 2); thus if the ratios of distances and times are determined, then so is the ratio of velocities. A definition of a unit of a physical quantity is a statement that determines the ratio of any instance of the quantity to the unit.
A closely related system is the International System of Electric and Magnetic Units, [18] which has a different unit of mass so that the formula for 𝜆′ is invalid. The unit of mass was chosen to remove powers of ten from contexts in which they were considered to be objectionable (e.g., P = VI and F = qE). Inevitably, the powers of ten ...
For historical reasons, the names and symbols for multiples and sub-multiples of the unit of mass are formed as if the gram were the base unit. Prefix names and symbols are attached to the unit name gram and the unit symbol g respectively. For example, 10 −6 kg is written milligram and mg, not microkilogram and μkg. [1]: 144
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
SI derived units are units of measurement derived from the seven SI base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem).
A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol (for kilogram). Quantities that are vectors have, besides numerical value ...