## 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

19 cm + 23 m + 25.9 m

It is necessary to first convert everything to the same units, let's say meters

0.19 m + 23 m + 25.9 m = 49.09 m

If you wanted, you could have converted everything to centimeters

19 cm + 2 300 cm + 2 590 cm = 4 909 cm

although it would probably be conventional, in most cases, to then state the final answer in meters, i.e.

49.09 m

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. (non-English 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

Quick Quiz

 Express in meters 1.     231 mm 2.     0.05 km 3.     131 cm 4.     5 km 5.     25 mm Express in centimeters 6.     23 mm 7.     0.4 km 8.     13 m 9.     0.05 km

### 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 - m2
• • square centimeters - cm2
• • square millimeters - mm2

For larger areas, the hectare is used - an area equivalent to the area of a square with sides of 100 meters.

(100 m)2 = 10 000 m2

This means that a square kilometer contains 100 hectares

so an area of 679 hectares = 6.79 km2

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 cm3 ( sometimes c.c. )

Note (for general background knowledge) a liter is equal to a decimeter cubed, usually stated as dm3, where a decimeter is one-tenth of a meter.

(1 dm)3 = ( 10 cm )3 = 10 x 10 x 10 cm3 = 1 000 cm3

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 introduced the Imperial system in 1824, standardising units for the British Empire, but obviously America had become independent by then.

It is worth noting that sometimes the older units exist slightly 'artificially' - for example a so-called 3.5 inch floppy disk is actually a 9 centimeter disk, as defined by International Standards.

And sometimes any 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

### History

The metric system is closely associated with Mathematics for the reason that it was drawn up by a committee of world-class 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 old-fashioned 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 led 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 hundredweight 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' little-used 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. 