Units and dimensions

Units and dimensions
Introduction
Base units and derived units
The SI system of units.

Introduction
In science, a type of question often asked is how much? how big? In order to answer such questions it is important to have systems of measurement which are consistent and understood by all.
A dimension is a property that can be measured such as distance, time, temperature, speed.
A unit is a basic division of a measured quantity and it enables to say how much of the quantity we have - 10 miles, 2 hours etc.

Base units and derived units
Basic units are units that are defined by reference to some external standard. This external standard is arbitrary but is a matter of common agreement.
Derived units are units that are defined by reference to combinations of the base units.

The SI system of units.
The SI system is an internationally agreed system of units based on seven base units. These are listed in table 1 below. Some of the more important derived units are listed in table 2.
Table 1
Base units of the SI system of unitsQuantity Unit Symbol Mass kilogramme kg Length metre m Time second s Mole mole mol Temperature kelvin K Electric current ampere A Light intensity candela cd

Table 2
Some derived units in the SI systemQuantity Unit Symbol Volume cubic metre m3 Force Newton = kg m s-2 N Pressure Pascal = N m-2 Pa Work, Energy Joule = N m J Power Watt = J s-1 W Molar concentration Molar = mol dm-3 or mol L-1 M

Multiples of the basic units are used to avoid having to write very large or very small numbers. These are listed in table 3.
Table 3
Multipliers for SI unitLarge quantities Small Quantities Prefix Symbol multiplier Prefix Symbol multiplier deca D 10 deci d 10-1 hecta h 100 centi c 10-2 kilo k 103 milli m 10-3 Mega M 106 micro m 10-6 Giga G 109 nano n 10-9 Tera T 1012 pico p 10-12 Exa E 1015 femto f 10-15

Dimensional consistency
All equations relating physical quantities should be dimensionally consistent. That is when the units on both sides of an equation are worked out they should be identical.
Example 1consider the ideal gas equation, Pv = nRT
Writing the units for each term in the equation
LHS: RHS:
i.e. LHS units = RHS units
If an equation contains additive terms, then each term in the equation must be dimensionally consistent.
Example 2The equation for the distance travelled by a body moving with uniform acceleration is;
s = u.t +1/2 a.t2
Writing the units for each term in the equation
i.e. Units of all three terms in the equation are the same.
source: wikipedia