The International System of Units
The Système International d'Unités, or International System of Units (abbreviated to S.I.) was adopted by Australia
after the Eleventh General Conference on Weights and Measures in 1960.
The S.I. consists of units (7 base units, 2 supplementary units, various derived units), and the
decimal multipliers for these units.
The base units are shown in the following table.
quantity 
unit name 
symbol 
definition now based on: 
length 
meter 
m 
the wavelength of light from Krypton86 
mass 
kilogram 
kg 
a mass placed in Paris in 1889 
time 
second 
s 
the time for an electron to move in an atom 
electric current 
Ampère 
A 
the force between two currents 
temperature 
Kelvin 
K 
1/273.16 of triple point of water 
luminous intensity 
candela 
cd 
the light falling on an area 
amount of substance 
mole 
mol 
0.012kg of Carbon12 
The supplementary units are
quantity 
unit name 
symbol 
definition now based on: 
plane angle 
radian 
rad 
arc length divided by radius 
solid angle 
steradian 
sr 
area divided by radius 
Derived units are numerous and will be explained as they are introduced. Some have special names, like frequency, force, and flux density.
A few examples of derived units
quantity 
unit name 
symbol 
area 
square metre 
m^{2} 
volume 
cubic metre 
m^{3} 
density 
kilogram per cubic metre 
kg.m^{3} 
speed 
metres per second 
m.s^{1} 
There are some units in popular or professional use, which are outside this system.
Some examples of these are: centimetre, hectopascal, hectare, kilometre per hour etc.
In this course, non standard units should be automatically converted before use.
Replace each nonstandard unit with its size in standard units then separate out the units and simplify.
Example:
5 c.c. = 5 cm^{3} = 5 x (10^{2} m)^{3} = 5 x 10^{6} m^{3}
72 km/hr = 72 (1000 m)/(3600 s) = 72 x (1/3.6) m.s^{1} = 20 m.s^{1}
The following decimal prefixes are based on multiples of 1000.
The full table is shown, but usually only the prefixes between Tera and pico are used.
Prefix 
Symbol 
Multiplier 
10^{+0 }= 1 
Prefix 
Symbol 
Divisor 
kilo 
k 
10^{+3} 

milli 
m 
10^{3} 
Mega 
M 
10^{+6} 

micro 
µ (Gk: mu)  10^{6} 
Giga 
G 
10^{+9} 

nano 
n 
10^{9} 
Tera 
T 
10^{+12} 

pico 
p 
10^{12} 
Peta 
P 
10^{+15} 

femto 
f 
10^{15} 
Exa 
E 
10^{+18} 

atto 
a 
10^{18} 
Zetta 
Z 
10^{+21} 

zepto 
z 
10^{21} 
Yotta 
Y 
10^{+24} 

yocto 
y 
10^{24} 
Standard form is a number between 1 and 10 multiplied by the appropriate power of ten, e.g. 3.1 x 10^{4} m.
Ternary form uses only the prefixes above and is the preferred form for this course, e.g. 310 µm.
Significant figures give the number of digits which establish the accuracy of the measurement.
For example, if the average radius of the Earth is given as 6360 km, this implies that the measurement is meaningful only to 10s of km.
Calculators give all the digits they can display, so calculator results should have the number of digits reduced to show the accuracy of the result.
The last digit should be rounded up (if the next digit is 5 or greater) or left as is (if the next digit is less than 5).
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