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Reference

Units

Concept

Base Units

A base unit, or fundamental unit, is a unit used for the measurement of a certain quantity. The International System of Units — the SI units — is a set of seven fundamental units agreed on as a system of units in the sciences.

SI Base Units
Quantity (symbol)	Name	Symbol
Mass (m)	kilogram	kg
Length (l)	meter	m
Time (t)	second	s
Temperature (T)	kelvin	K
Electric current (I)	ampere	A
Luminous intensity (I_v)	candela	cd
Amount of substance (n)	mole	mol

Through multiplications and divisions, the base units can be used to define other units called derived units. One example is velocity (m/s). However, base units cannot themselves be derived from other units.

Extra

Imperial Units

Apart from the SI base units, there are other systems that use different units of measurement, like the Imperial System of Units.

Imperial Units
Quantity	Common Units
Mass	ounce, pound, ton
Length	inch, foot, mile
Area	square foot, square yard, square mile
Volume	pint, quart, gallon

Concept

Derived Units

Derived units are units of measurement formed by multiplying or dividing base units in different combinations.

Quantity (Symbol)	Expression	Base Units	Unit Symbol (Name)
Area (A)	length * width	m^2	m^2
Volume (V)	area * height	m^3	m^3
Speed (r)	distance/time	.m /s.	.m /s.
Acceleration (a)	speed/time	.m /s^2.	.m /s^2.
Density ( )	mass/length^3	.kg /m^3.	.kg /m^3.
Force (F)	mass * acceleration	.kg* m /s^2.	N (newton)
Pressure (P)	force/area	.N /m^2.	Pa (pascal)
Energy (E)	force * distance	N*m	J (joule)
Power (P)	force* distance/time	.J /s.	W (watt)
Frequency (F)	1/time	.1 /s.	Hz (hertz)

The derived units shown in this table are only some of the many possible combinations of base units.

Concept

Customary System

The customary system is the measurement system most commonly used in the United States. This system of measurement contains units for length, capacity, and weight. For example, the inch is a unit of length, the ounce is a unit of weight, and the quart is a unit of volume. Examples of Units in the Customary System inch, ounce, and quart The table shows the relationship between units of each measure type in the customary system.

Customary Units
Type	Unit	Equivalent Unit
Length	1 foot (ft)	12 inches (in.)
	1 yard (yd)	3ft
	1 mile (mi)	5280ft
Weight	1 pound (lb)	16 ounces (oz)
Weight	1 ton (T)	2000 lb
Volume	1 cup (c)	8 fluid ounces (fl oz)
	1 pint (pt)	2c
	1 quart (qt)	2pt
	1 gallon (gal)	4qt

Converting measures requires using the appropriate conversion factors.

Concept

Metric System

The metric system is a measurement system commonly in most countries around the world. The base units in the metric system are meters for length, liters for capacity, and kilograms for weight. Base Units in Metric System meter, liter, and kilogram In the metric system, units are related by powers of 10. Metric units are named by adding metric prefixes to the base units.

Metric Units of Length

The table shows the commonly used metric units of length.

Unit	Equivalent Unit
1000 millimeters (mm)	1 meter (m)
100 centimeters (cm)	1m
10 decimeters (dm)	1m
1 dekameter (dam)	10m
1 hectometer (hm)	100m
1 kilometer (km)	1000m

Metric Units of Capacity

For measuring capacity, the metric system uses the liter as the base unit.

Unit	Equivalent Unit
1000 milliliters (mL)	1 liter (L)
100 centiliters (cL)	1L
10 deciliters (dL)	1L
1 dekaliter (daL)	10L
1 hectoliter (hL)	100L
1 kiloliter (kL)	1000L

Metric Units of Weight

In the metric system, kilogram, gram, and milligram are some commonly used units for measuring weight.

Unit	Equivalent Unit
1000 milligrams (mg)	1 gram (g)
100 centigrams (cg)	1g
10 decigrams (dg)	1g
1 dekagram (dag)	10g
1 hectogram (hg)	100g
1 kilogram (kg)	1000g

Notice that each relationship in the tables can be written as a ratio. These ratios can be considered conversion factors.

Concept

Conversion Factor

A conversion factor is a fraction where the numerator and denominator represent the same quantity with different units. Example Conversion Factor [0.5em] 60 minutes/1 hour Recall that 1 hour and 60 minutes represent the same quantity. Multiplying a quantity by a conversion factor changes the quantity to an equivalent quantity in different units.

Given Quantity	Conversion	Result
2 hours	2 hours * 60 minutes/1 hour	120 minutes

The process of including units of measurement as factors is called dimensional analysis. Dimensional analysis can also be used when deciding which conversion factor will produce the target units.

Why

The Reason That the Quantities Are Equivalent

The numerator and denominator of the conversion factor represent the same quantity. This means that their quotient equals 1. Then, by the Identity Property of Multiplication, the amount of the given quantity does not change when multiplied by the conversion factor. Given Amount * 1 = Given Amount When converting from one unit to another, the target unit needs to be in the numerator of the conversion factor and the given unit needs to be in the denominator. Then when the quantity is multiplied by the conversion factor, the given unit will cancel out and the target unit will remain.

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