Everything about The Metric System totally explained
The
metric system is a decimalised
system of measurement. It exists in several variations, with different choices of
base units, though the choice of base units doesn't affect its day-to-day use. Over the last two centuries, different variants have been considered
the metric system. Since the 1960s the
International System of Units (SI) ("
Système International d'Unités" in
French, hence "SI") has been the internationally recognised
standard metric system. Metric units are widely used around the world for personal, commercial and scientific purposes. A standard set of prefixes in multiples of 10 may be used to derive larger and smaller units. However, the prefixes for multiples of 1000 are the most commonly used.
Overview
One goal of the metric system is to have a single unit for any physical quantity; another important one isn't needing conversion factors when making calculations with physical quantities. All lengths and distances, for example, are measured in metres, or thousandths of a metre (millimetres), or thousands of metres (kilometres), and so on. There is no profusion of different units with different conversion factors, such as
inches,
feet,
yards,
fathoms,
rods,
chains,
furlongs,
miles,
nautical miles,
leagues, etc. Multiples and submultiples are related to the fundamental unit by factors of powers of ten, so that one can convert by simply moving the decimal place: 1.234 metres is 1234 millimetres, 0.001234 kilometres, etc. The use of
fractions, such as of a metre, isn't prohibited, but uncommon, as it's generally not necessary.
The original metric system was intended to be used with the time units of the
French Republican Calendar, but these fell into disuse. Today
decimal time isn't in everyday use. Submultiples of the second (the microsecond for example) are used in scientific work but for lengths of time greater than a second traditional units, with their non-decimal conversion factors, are more often used than decimal multiples of the second.
In the late 18th century,
Louis XVI of
France charged a group of experts to develop a unified, natural and universal system of measurement to replace the disparate systems then in use. This group, which included such notables as
Lavoisier, produced the metric system, which was then adopted by the revolutionary government of France. In the early metric system, there were several fundamental or base units, the
grad or
grade for angles, the
metre for length, the
gram for mass and the
litre for capacity. These were derived from each other via the properties of natural objects, mainly the
Earth and
water: 1 metre was originally defined as of the polar
circumference of the Earth, the
kilogram was originally defined as the mass of one litre (or, equivalently, 1 dm³) of water at its melting point (this definition was later revised to specify a temperature of 4 °C). The
Celsius temperature scale was derived from the properties of water, with 0 °C being defined as its freezing point and 100 °C being defined as its boiling point under a pressure of one
standard atmosphere.
The
metre was later redefined as the length of a particular bar of
platinum-
iridium alloy; then in terms of the
wavelength of light emitted by a specified atomic transition; and now is defined as the
distance travelled by light in an absolute vacuum during of a second. The
gram, originally one millionth of the mass of a cubic metre of water, is currently defined by one thousandth of the mass of a specific object that's kept in a vault in France; however there are efforts underway to redefine it in terms of physical quantities that could be reproduced in any laboratory with suitable equipment. The
second, originally of the mean
solar day was redefined in 1967 to be 9,192,631,770 periods of vibration of the radiation emitted at a specific wavelength by an atom of caesium-133. Varying choices have been made for the fourth base unit, that which is needed to incorporate the field of electromagnetics; As of 2006, this is the
ampere, being the base unit of electrical current. Other quantities are derived from the base units; for example, the basic unit of
speed is metres per second. As each new definition is introduced, it's designed to match the previous definition as precisely as possible, so these changes of definition have not affected most practical applications. (
See SI and individual unit articles for full definitions.)
The names of multiples and submultiples are formed with
prefixes. They include
deca- (ten),
hecto- (hundred),
kilo- (thousand),
mega- (million), and
giga- (billion);
deci- (tenth),
centi- (hundredth),
milli- (thousandth),
micro- (millionth), and
nano- (billionth). The most commonly used prefixes for multiples depend on the application and sometimes tradition. For example, long distances are stated in thousands of kilometres, not megametres.
Most everyday users of the metric system measure
temperature in degrees
Celsius, though the SI unit is the
kelvin, a scale whose units have the same "size", but which starts at
absolute zero. Zero degrees Celsius equals 273.15 kelvins (the word "degree" is no longer to be used with kelvins since 1967-1968).
Angular measurements have been decimalised, but the older non-decimal units of angle are far more widely used. The decimal unit, which isn't part of SI, is the
gon or
grad, equal to one hundredth of a
right angle. Subunits are named, rather than prefixed: the
gon is divided into 100
decimal minutes, each of 100
decimal seconds. The traditional system, originally Babylonian, has 360
degrees in a
circle, 60
minutes of arc (also called arcminutes) in a degree, and 60
seconds of arc (also called arcseconds) in a minute. The clarifier "of arc" is dropped if it's clear from the context that we're not speaking of minutes and seconds of time. Sometimes angles are given as decimal degrees, for example, 26.4586 degrees, or in other units such as
radians (especially in scientific uses other than
astronomy) or
angular mils.
History
In 1586, the
Flemish mathematician
Simon Stevin published a small pamphlet called
De Thiende ("the tenth"). Decimal fractions had been employed for the extraction of square roots some five centuries before his time, but nobody established their daily use before Stevin. He felt that this innovation was so significant that he declared the universal introduction of decimal coinage, measures and weights to be merely a question of time.
The idea of a metric system has been attributed to
John Wilkins, first secretary of the
Royal Society of London in 1668. The idea didn't catch on, and England continued with its existing system of various weights and measures.
In 1670
Gabriel Mouton, a French abbot and scientist, proposed a decimal system of measurement based on the circumference of the Earth. His suggestion was a unit, milliare, that was defined as a minute of arc along a meridian. He then suggested a system of sub-units, dividing successively by factors of ten into the centuria, decuria, virga, virgula, decima, centesima, and millesima.
His ideas attracted interest at the time, and were supported by Jean Picard as well as Huygens in 1673, and also studied at Royal Society in London. In 1673,
Gottfried Leibniz independently made proposals similar to those of Mouton.
The proliferation of disparate measurement systems was one of the most frequent causes of disputes amongst merchants and between citizens and tax collectors. A unified country with a single currency and a countrywide market, as most European countries were becoming by the end of the 18th century, had a very strong economic incentive and was in a position to break with this situation and standardise on a measuring system. The inconsistency problem wasn't one of
different units but one of
differing sized units so instead of simply standardising size of the existing units, the leaders of the French revolutionary governments decided that a completely new system should be adopted.
The first official adoption of such a system occurred in
France in 1791 after the
French Revolution of 1789. The creators of this metric system tried to choose units that were logical and practical. The revolution gave an opportunity for drastic change with an official ideology of "pure reason". It was proposed as a considerable improvement over the inconsistent collection of customary units that existed before, and that it be based on units of ten, because scientists, engineers, and bureaucrats at the time found this more convenient for the complex unit conversion they often must do.
The adoption of the metric system in France was slow, but its desirability as an international system was advocated by
geodesists and others. Since then a number of variations on the system evolved. Their use spread throughout the world, first to the non-English-speaking countries, and more recently to the English-speaking countries.
The whole system was derived from the properties of natural objects, namely the size of the Earth and the density of water, and simple relations in between one unit and the other. In order to determine as precisely as possible the size of the Earth, several teams were sent over several years to measure the length of as long a segment of a
meridian as feasible. It was decided to measure the
meridian spanning
Barcelona and
Dunkirk which was the longest segment almost fully over land within French territory. It should be noted that even though, during the many years of the measurement, hostilities broke out between
France and
Spain, the development of such a standard was considered of such value that Spanish troops escorted the French team while in Spanish territory to ensure their safety.
The whole process ended in the proclamation on
June 22,
1799 of the metric system with the storage in the Archives of the Republic of the physical embodiments of the standard, the prototype metre and the prototype kilogram, both made in a platinum alloy, witnessed by representatives of the French and several foreign governments and most important
natural philosophers of the time. The motto adopted for the metric system was: "for all men, for all time".
In revolutionary France the system wasn't particularly well accepted, and the old units, now illegal, remained in widespread use. On
February 12 1812, Napoleon, who had other concerns than enforcement of the system, authorised the usage of
Mesures usuelles, traditional French measures redefined on the base of Metric System (
toise as 2 metres,
livre as 500 grams, etc.), and finally in 1816 a law made these
Mesures usuelles standards. This law was cancelled in 1825 and the metric system reinstated fully in 1837. It had already been reinstated in 1820 by a somewhat unlikely person, King William I of the neighbouring (United) Netherlands. Although he was generally considered more conservative, he was desperate to bring at least some form of unity to his rather disunited kingdom and stimulate the industrial development of the South. Although the imposed system was metric, a number of old local names like 'pond' (pound) and 'ons' (ounce) were substituted for 500 g and 100 g respectively, and although they were officially abolished in the 1870s, they survive to the present day. The king's attempts were in vain in that Belgium claimed its independence from the Netherlands, but the metric system survived and began a slow but steady conquest of the world. By the 1960s, the majority of nations were on the metric system and most that were not had started programmes to fully convert to the metric system (
metrication). As of 2007 only three countries, the
United States,
Liberia, and
Myanmar (Burma) hadn't mandated the metric system upon their populace.
Later improvements in the measurement of both the size of the Earth and the properties of water revealed discrepancies between the metric standards and their originally intended values. The
Industrial Revolution was well under way and the standardisation of mechanical parts, mainly bolts and nuts, was of great importance and they relied on precise measurements. Though these discrepancies would be mostly hidden in the manufacturing tolerances of those days, changing the prototypes to conform to the new and more precise measurements would have been impractical particularly since new and improved instruments would continually change them.
It was decided to break the linkage between the prototypes and the natural properties they were derived from. The prototypes then became the basis of the system. The use of prototypes, however, is problematic for a number of reasons. There is the potential for loss, damage or destruction. There is also the problem of variance of the standard with the changes that any artifact can be expected to go through, though they be slight. Also whilst there may be copies, there must be only one official prototype which can't be universally accessible.
The metre had been defined in terms of such a prototype and remained so until 1960. At that time, the metre was defined as a certain number of wavelengths of a particular frequency of light emitted by a certain element. Since 1983 the metre has been defined as the distance light travels in a given fraction of a second in a vacuum. Thus the definition of the metre ultimately regained a linkage with a natural property, this time a property thought immutable in our universe and truly universal. The
kilogram is now the only base unit still defined in terms of a prototype. Since 1899, the kilogram has been formally anchored to a single platinum-iridium cylinder in Sèvres, France.
On
May 20 1875 an international treaty known as the
Convention du Mètre (Metre Convention) was signed by 17 states (including the United States). This treaty established the following organisations to conduct international activities relating to a uniform system for measurements:
- Conférence générale des poids et mesures (CGPM), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
- Comité international des poids et mesures (CIPM), consisting of selected scientists and metrologists, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the International Bureau of Weights and Measures;
- Bureau international des poids et mesures (BIPM), a permanent laboratory and world centre of scientific metrology, the activities of which include the establishment of the basic standards and scales of the principal physical quantities and maintenance of the international prototype standards.
The metric system is used widely for scientific purposes but there are some exceptions, especially at large and small scales, such as the
parsec. It has been adopted for everyday life by most nations through a process called
metrication. As of 2006, 95% of the world's population live in metricated countries, although non-metric units are still used for some purposes in some countries. The holdouts to full metrication are the
United States and, to a lesser degree, the
United Kingdom, where there's public attachment to the traditional units.
Goals
The metric system was designed with several goals in mind.
Neutral and universal
The designers of the metric system meant to make it as neutral as possible so that it could be adopted universally.
Replicable
The usual way to establish a standard was to make prototypes of the base units and distribute copies. This would make the new standard reliant on the original prototypes which would be in conflict with the previous goal since all countries would have to refer to the one holding the prototypes.
The designers developed definitions of the base units such that any laboratory equipped with proper instruments should be able to make their own models of them. The original base units of the metric system could be derived from the length of a
meridian of the Earth and the weight of a certain volume of pure water. They discarded the use of a
pendulum since its period or, inversely, the length of the string holding the bob for the same period changes around the Earth. Likewise, they discarded using the circumference of the Earth over the Equator since not all countries have access to the Equator while all countries have access to a section of a meridian.
Decimal multiples
The metric system is decimal, in the sense that all multiples and submultiples of the base units are factors of powers of ten of the unit. Fractions of a unit (for example 29/64) are not used formally. The practical benefits of a decimal system are such that it has been used to replace other non-decimal systems outside the metric system of measurements; for example currencies.
The simplicity of decimal prefixes encouraged the adoption of the metric system. Clearly the advantages of decimal prefixes derive from our using
base 10 arithmetic, a consequence of our happening to have 10 digits (fingers and thumbs). At most, differences in expressing results are simply a matter of shifting the decimal point or changing an exponent; for example, the
speed of light may be expressed as 299 792.458 km/s or 2.99792458×10
8 m/s.
Prefixes
All derived units would use a common set of prefixes for each multiple. Thus the prefix
kilo could be used both for mass (
kilogram) or length (
kilometre) both indicating a thousand times the base unit. This didn't prevent the popular use of names for some derived units such as the
tonne which is a
megagram while a
quintal is accepted as 100 kilograms; both are derived from old customary units and were rounded to metric.
The function of the prefix is to multiply or divide the measure by a factor of ten, one hundred or a positive integer power of one thousand. If the prefix is Greek-derived, the measure is multiplied by this factor. If the prefix is Latin-derived, it's divided. The Greek prefix
kilo~ and the Latin prefixes
centi~ and
milli~ are those most familiar from everyday use.
Examples:
|
| metre |
|
(common base unit) |
| decametre |
= 10 metres |
(a measure used in naval artillery) |
| hectometre |
= 100 metres |
(not commonly used) |
| kilometre |
= 1000 metres |
| decimetre |
= of a metre |
| centimetre |
= of a metre |
| millimetre |
= of a metre |
| litre |
|
(common base unit) |
| decalitre |
= 10 litres |
(not a commonly used measure) |
| hectolitre |
= 100 litres |
(used for beer kegs, 1 keg is approx. of a hectolitre) |
| kilolitre |
= 1000 litres |
(not commonly used) |
| decilitre |
= of a litre |
| centilitre |
= of a litre |
| millilitre |
= of a litre |
A similar application of Greek and Latin prefixes can be made with other metric measurements.
Relation of volume and mass of water
Originally, units for volume and mass were directly related to each, with mass defined in terms of a volume of
water. Even though that definition is no longer used, the relation is quite close at room temperature and nearly exact at 4 °C. So as a practical matter, one can fill a container with water and weigh it to get the volume, for example.
Relations:
|
| 1000 litres |
= 1 cubic metre |
≈ 1 tonne of water |
("cubic metre" is commonly used instead of "kilolitre") |
| 1 litre |
= 1 cubic decimetre |
≈ 1 kilogram of water |
| 1 millilitre |
= 1 cubic centimetre |
≈ 1 gram of water |
| 1 microlitre |
= 1 cubic millimetre |
≈ 1 milligram of water |
Practical
The base units were chosen to be of similar magnitude to customary units. The metre, being close to half a
toise (French
yard equivalent), became more popular than the failed decimal hour of the Republican Calendar which was 2.4 times the normal hour.
The kilometre was originally defined as the length of an arc spanning a decimal minute of
latitude, a similar definition to that of the
nautical mile which was the length of an arc of one (non-decimal) minute of
latitude.
Coincidental similarities to real-life values
Two important values, when they were expressed in the metric system, turned out to be very close to a multiple of 10. The standard acceleration due to gravity on Earth g
n has been defined to be 9.80665
m/
s² exactly, which is the value at about 45° north or south of the equator. Accordingly the
force exerted on a
mass of one kilogram in Earth gravity (
F = m·a) is about ten newtons (kg-m/s²). This simplified the metrication of many machines such as locomotives, which were simply re-labelled from for example "85
tonnes" to "850 kN". A closer approximation is π² m/s², which means a one-metre
pendulum has a period of almost exactly two seconds.
Also, the standard
atmospheric pressure, previously expressed in
atmospheres, when given in
pascals, is 101.325 kPa. Since the difference between 10 atmospheres and 1 MPa is only 1.3%, many devices were simply re-labeled by dividing the scale by ten, for example 1 atm was changed to 0.1 MPa.
In addition, the
speed of light in a vacuum turns out to be astonishingly close (0.07% error) to 3×10
8 m/s.
A useful conversion used in meteorology is 1 m/s ≈ 2
knots with less than a 3% error, actually 1.94384 knots (to 5 decimal places). The equivalent conversion for distance isn't so "rounded", 1
nautical mile = 1.852 km (exactly) = 1 minute of arc
Latitude (approximately).
Metric systems
Original system
The metric system, and metre was first fully described by Englishman John Wilkins in 1668 in a treatise presented to the Royal Society some 120 years before the French adopted the system.
It is believed that the system was transmitted to France from England via the likes of Benjamin Franklin (who spent a great deal of time in London), and produced the by-product of the decimalised paper currency system, before finding favour with American revolutionary ally Louis XV.
The original French system continued the tradition of having separate base units for geometrically related dimensions, for example
metre for lengths,
are (100 m²) for areas,
stere (1 m³) for dry capacities and
litre (1 dm³) for liquid capacities. The
hectare, equal to a hundred
ares, is the area of a square 100 metres on a side (about 2.5
acres), and is still in use to measure fields.
The base unit of mass is the
kilogram. This is the only base unit that has a prefix, for historical reasons. Originally the kilogram was called the "grave", and the "gramme" was an alternative name for a thousandth of a grave. After the French Revolution, the word "grave" carried negative connotations, as a synonym for the title "count". The grave was renamed the kilogram. This also serves as the prototype in the
SI. It included only few
prefixes from
milli, one thousandth to
myria ten thousand.
Several national variants existed thereof with aliases for some common subdivisions. In general this entailed a redefinition of other units in use, for example 500-gram
pounds or 10-kilometre miles or leagues. An example of these is
mesures usuelles. However it's debatable whether such systems are true metric systems.
Centimetre-gram-second systems
Early on in the history of the metric system various
centimetre gram second systems of units (CGS) had been in use. These units were particularly convenient in science and technology. For example, in CGS the density of water is approximately 1 gram per cubic centimetre.
Metre-kilogram-second systems
Later metric systems were based on the
metre,
kilogram and
second (MKS) to improve the value of the units for practical applications. Metre-kilogram-second-
coulomb (MKSC) and metre-kilogram-second-
ampere (MKSA) systems are extensions of these.
The
International System of Units (
Système international d'unités or SI) is the current international standard metric system and the system most widely used around the world. It is based on the metre, kilogram, second, ampere,
kelvin,
candela and
mole.
Metre-tonne-second systems
The
metre-tonne-second system of units (MTS) was based on the metre,
tonne and second. It was invented in France and mostly used in the
Soviet Union from 1933 to 1955.
Gravitational systems
Gravitational metric systems use the
kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the
hyl, TME, mug or
metric slug. Note these are not part of the
International System of Units (SI).
Variations in terminology
In keeping with
American English spelling,
meter,
liter, etc. are used in the United States. In addition, the official US spelling for the rarely used
SI prefix for ten is
deka. In American English the term
metric ton is the normal usage whereas in other varieties of English
tonne is common.
The US government has approved this terminology for official use. In scientific contexts only the symbols are used; since these are universally the same, the differences don't arise in practice in scientific use.
Gram is also sometimes spelled
gramme in English-speaking countries other than the United States, though it's an older spelling and its usage is declining.
Conversion and calculation errors
Gimli Glider — In 1983 a Boeing 767 jet ran out of fuel in midflight because of two mistakes in figuring the fuel supply of Air Canada's first aircraft to use metric measurements.
Mars Climate Orbiter — In 1999 NASA lost a $125 million Mars orbiter because one engineering team used metric units while another used US customary units for a calculation.
Notes and references
Further Information
Get more info on 'Metric System'.
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