Units of Measurement
Introduction
The metric system uses a straightforward decimal system. Conversion between different units of measurement ( e.g. between meters and centimeters ) only involves shifting the decimal point.
Likewise, mathematical operations are carried out in the same way as normal decimal number operations. But make absolutely certain that the quantities involved in the calculations are all expressed in the same units.
Example : Consider
It is necessary to first convert everything to the same units, let's say meters
If you wanted, you could have converted everything to centimeters
although it would probably be conventional, in most cases, to then state the final answer
in meters, i.e.
the conversion from centimeters to meters involving shifting the decimal
point by two places to the left (the decimal point was implied in 4 909 cm., not actually
shown explicitly ).
Length
The basic unit of length is the meter. The names of other lengths are derived using the
following formulation, the same formulation being used for units of other quantities as well.
1 000 meters  kilometer 
100 meters  hectometer 
10 meters  decameter 
1 meter  meter 
0.1 meter  decimeter 
0.01 meter  centimeter 
0.001 meter  millimeter 
Note : kilometers per hour is conventionally abbreviated as km/h, not k.p.h. (nonEnglish speaking countries will not recognize this latter form)
A4 paper is 210 mm wide and about 300 mm high (actually 297 mm)
Most people are between 1.4 meters and 1.8 meters in height.
Snowdon / Yr Wyddfa  1085 meters 
Ben Nevis: 1343 meters  
Mont Blanc: 4807 meters  
Mount Everest: 8850 meters 

Weight (or Mass)
The basic unit of weight (strictly speaking, mass) is the gram. Using the same
formulation as above
will produce
1 000 grams  kilogram 
100 grams  hectogram 
10 grams  decagram 
1 gram  GRAM 
0.1 gram  decigram 
0.01 gram  centigram 
0.001 gram  milligram 
Note : 1 000 kg equals one metric tonne
Area
The area of a shape is a measure of how many square units it contains. The units employed would be typically
 • square meters  m^{2}
 • square centimeters  cm^{2}
 • square millimeters  mm^{2}
For larger areas, the hectare is used  an area equivalent to the area of a square
with sides of 100 meters.
This means that a square kilometer contains 100 hectares
Note that, in the case of area, conversion to different units is more complicated than
with 'straightforward' length.
For example, a square kilometer is 1 000 000 times as large as a square meter ( NOT 1 000 times as large ).
Consider squares for simplicity  each side of a square kilometer will be 1 000 times as long as a square meter, and by multiplying 1 000 by 1 000 you can see that a square kilometer is indeed 1 000 000 (1 million) times as large as a square meter.
Volume
The common unit of volume is the liter. This is, as expected, composed of 1 000 milliliters.
A milliliter (ml) is also a cubic centimeter, which has the abbreviation cm^{3} ( sometimes c.c. )
Note (for general background knowledge) a liter is equal to a decimeter cubed, usually stated as dm^{3}, where a decimeter is onetenth of a meter.
which equals 1 liter, as already stated.
One liter of water weighs one kilogram
Temperature
Water freezes at 0 degrees, so we commonly encounter negative numbers in
connection with temperature (see the
Negative Numbers module).
Water will boil at 100 degrees
Body temperature is 36.9 degrees (on average).
Old Units
The older Imperial units are now often officially defined in terms of metric units. For
example 1 inch is defined as 2.54 centimeters exactly. Conversion proceeds in a manner
similar to currency conversion.
 5 inches = 5 x 2.54 cm = 12. 7 cm
 2.65 inches = 2.65 x 2.54 cm = 6.731 cm
 30 cm = 30 / 2.54 ins = 11.81 (to 2 decimal places)
 3.56 cm = 3.56 / 2.54 ins = 1.40 ins ( to 2 decimal places )
A pint is equal to 568 ml, although that is only for the British pint  pints and gallons have a
different meaning in the USA. This was because the British Government changed
the standards in the 19th. Century, leaving America operating on the original standards.
It is worth noting that sometimes the older units exist slightly 'artificially'  for example a socalled 3.5 inch floppy disk is actually a 9 centimeter disk, as defined by International Standards.
And sometimes the imperial sizes stated are even further from their actual size  the sizes of TV screens, when they are given in inches, have a tendency to be 'approximate'.
Think Metric
Diameter of Floppy Disk  9cm 
Diameter of CD  12cm 
Width of A4  21cm 
Depth of A4  29.7cm 
1 liter of milk  approx 1 kg 
Links
History
The metric system is closely associated with Mathematics for the reason that it was
drawn up by a committee of worldclass mathematicians  people like Laplace, Lagrange, Carnot.
It was ready by 1799 and although not enjoying a fully continuous use since that date, it did eventually establish itself not just as the standard system in France but also came to dominate the world (which it has done for over a hundred years now).
The names of oldfashioned units do sometimes still live on figuratively or adapted to nice round metric units. But the original problem was that different units with the same name varied from region to region. A mile originally came into being because the Romans had the 'lunatic' idea of actually having a basic idea of length composed of 1 000 units. I am lead to believe that by the 18/19 th. century some countries' miles were as much as eight times as long as Britain's. Even today we have a nautical mile in use in some quarters which is different from the mile used on land in Britain. You can sometimes hear the word 'pied' used for very short distances in France  I believe they got rid of the pound currency (livre) just by the simple expendient of renaming it 'franc'. A hundred weight in Deutschland is 50kg, while in Austria it is 100kg  but this doesn't cause any difficulties. It's a bit like when I lived in Liverpool and everyone used the word 'gill' to refer to half a pint, whereas the reference books said that a gill was a quarter of a pint  it was an 'unofficial' unit, everyone knew that it was different elsewhere, so no confusion ensued.
The SI system lays down the rules for use of metric units, primarily in science. Essentially it defines the combination of units to be used, e.g. the SI unit of force is the Newton, which is defined in terms of meters, kilograms and seconds as opposed to an older alternative metric convention where the unit of force was the dyne defined in terms of the centimeter, gram and second.
Some metric units have always had some sort of an existence in Britain, e.g. (Kilo)Watts which, in line with the SI convention, are defined in terms of meters, kilograms and seconds.