### 1.8: Measurement: Derived Units

The International System of Units or SI system, by international agreement, has fixed measurement units for seven fundamental properties: length, mass, time, temperature, electric current, amount of substance, and luminosity. These are called the SI base units.

Units of measurement derived from the mathematical combination of SI base units are called SI-derived units. For example, the ratio of the SI unit for distance (meter; m) and the SI unit for time (second; s) gives the SI-derived unit for speed (meter per second; m/s). Another common way of expressing the speed of an object is using miles per hour (miles/hour). Miles per hour is also considered a derived unit, even though the base units are not SI units. In general, any derived unit is a combination of other units.

#### Derived Units: Volume and Density

Volume is the measure of the amount of space occupied by an object. The unit of length defines the unit of volume.

The SI-derived unit of volume is a cubic meter (m^{3}), a cube with an edge length of exactly one meter. To dispense a cubic meter of water, we could build a cubic box with edge lengths of exactly one meter. This box would hold a cubic meter of water or any other substance.

Other common units of volume are the cubic decimeter (dm^{3}) and the cubic centimeter (cm^{3}). A cube with edge lengths of exactly one decimeter (or 10 cm) contains a volume of one cubic decimeter (1 dm^{3} or 1000 cm^{3}). A liter (L) is the more common name for the cubic decimeter. One liter is equal to 1000 milliliters, and one milliliter is equal to 1 cubic centimeter.

The density of a substance is the ratio of the mass of the substance to its volume

Thus, the units of density are defined by the units of mass and length (volume = length^{3}). Since the SI unit of mass is the kilogram (kg) and volume is the cubic meter (m^{3}), the SI-derived unit for density is the kilogram per cubic meter (kg/m^{3}).

Another common unit, grams per cubic centimeter (g/cm^{3}) is often used for the densities of solids and liquids, and grams per liter (g/L) for gases.

#### Extensive and Intensive Properties of Matter

A measurement unit expresses the magnitude of a physical quantity that is used to define a physical property of matter. Physical properties can be extensive or intensive. If the property depends on the amount of matter present, it is an extensive property. Extensive properties include mass, weight, and volume. For example, a liter of milk has a larger mass than a cup of milk. The value of an extensive property is directly proportional to the amount of matter in question. On the contrary, if the property does not depend on the amount of matter present, it is an intensive property. Temperature is an example of an intensive property. If one liter of milk and one cup of milk are each at 20 °C, their temperature remains at 20 °C when they are combined. Consider another example to understand the distinct but related properties of heat and temperature. A drop of hot cooking oil splattered on your arm causes brief, minor discomfort, whereas a pot of hot oil yields severe burns. Both the drop and the pot of oil are at the same temperature (an intensive property), but the pot of oil contains much more heat (extensive property).

*This text is adapted from Openstax, Chemistry 2e, Section 1.3: Physical and Chemical Properties and Openstax, Chemistry 2e, Section 1.4: Measurements.*