WEEK 8

The Metric System

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.[4][5][6] The idea did not 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 the Royal Society in London. In 1673,

Gottfried Leibniz independently made proposals similar to those of Mouton.

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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 to break with this situation and standardise on a measuring system.

The inconsistency problem was not one of different units but one of differing sized units.

Instead of simply standardising the size of the existing units, the leaders of the French

revolutionary Assemblée Constituante decided that a completely new system should be

adopted. It was felt that no country would accept standardizing on the units of another

country, but that there would be less resistance if a completely new system made

change compulsory for all countries.[citation needed]

Metric seal

On May 20, 1875 an international treaty known as the Convention du Mètre (Metre

Convention) was signed by 17 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;

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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.

Replicable Prototypes

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.

Instead, 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. For a time, the

Assemblée Constituante considered using the length of a pendulum beating the second

in Paris as the base of the metre; when they heard that the British Parliament was

discussing a similar proposal, based on the length of the pendulum beating the second

in London, the Assemblée contacted their counterparts in London and offered to

standardize on the London pendulum. Instead, the UK abandoned the idea of

metrication for another two centuries, and the meridian definition of the metre was

adopted[7]. The pendulum was not a likely choice for a prototype in any case, 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.[citation needed]

WEEK 8

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 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. 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 2.99792458×108 m/s.

Prefixes

All derived units would use a common set of prefixes for each multiple. Thus the

prefix kilo could be used for mass (kilogram) or length (kilometre) both indicating a

thousand times the base unit. This did not prevent the popular use of names for some

derived units such as the tonne which is a megagram; derived from old customary units

and 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.[8] If the prefix is Greek-

derived, the measure is a positive power. If the prefix is Latin-derived, it is a negative

power, except by 10-6 (micro~) which is also Greek-derived. The Greek prefix kilo~ and

the Latin prefixes centi~ and milli~ are those most familiar from everyday use.

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metre

Unit Relation to

base

megametr

e

106 metres

kilometre 103 metres

hectometre 102 metres

decametre 101 metres

decimetre 10-1 metrea

centimetre 10-2 metres

millimetre 10-3 metres

micrometre 10-6 metres

nanometre 10-9 metres

picometre 10-12 metres

litre

Unit Relation to

base

megalitre 106 litres

kilolitre 103 litres

hectolitre 102 litres

decalitre 101 litres

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decilitre 10-1 litres

centilitre 10-2 litres

millilitre 10-3 litres

microlitre 10-6 litres

A similar application of Greek and Latin prefixes can be made with other metric

measurements.

Practicality

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.

Originally, units for volume and mass were directly related to each other, 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,

1,000 litres = 1 cubic metre ≈ 1 tonne of water

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

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Coincidental similarities

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 gn 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 e.g. "85

tonnes" to "850 kN". A closer approximation is π2 (≈ 9.86960) m/s2, which means a one-

metre pendulum has a period of almost 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-labelled by dividing the scale by

ten, 1 atm was changed to 0.1 MPa.

In addition, the speed of light in a vacuum turned out to be astonishingly close (0.07%

different) to 3×108 m/s; the exact value, 299,792,458, has since become the definition.

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 is

not so "rounded", 1 nautical mile = 1.852 km (exactly) = 1 minute of arc Latitude

(approximately).

WEEK 8

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 favor with American revolutionary ally Louis XVI.[10]

The original French system continued the tradition of having separate base units

for geometrically related dimensions, i.e. metre for lengths, are (100 m2) for areas, stère

(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.

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 "gram" 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.[11] 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, e.g. 500-gram

pounds or 10-kilometre miles or leagues. An example of these is measures usuelles.

However it is debatable whether such systems are true metric systems.

WEEK 8

Centimetre-gram-second systems

Early on in the history of the metric system, various versions of centimetre gram

second system 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 one 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 (System international units 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).

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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 do not arise in practice in scientific use.

Gram is also sometimes spelled gramme in English-speaking countries other

than the United States, though it is an older spelling and its usage is declining.

Conversion and calculation errors

Cargo errors

The confusion between pounds (mass) and kilograms sometimes means that

aircraft are overloaded. "the shipper's weights had been in kilograms, not

pounds, and that, as a result, the aircraft was more than 30,000 pounds

overweight".

Gimli Glider

In 1983 a Boeing 767 jet ran out of fuel in mid-flight 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.

WEEK 8

Medical errors

Medical errors in the US are sometimes attributed to the confusion between

grains and grams. A patient received phenobarbital 0.5 grams instead of 0.5

grains (0.03 grams) after the prescriber misread the prescription.

WEEK 8

From: http://www.uffda.com/~bink/metric.html

The Metric System

The modern metric system of units and standards of measure is rooted in 17th-

and-18th century efforts to establish a simple, easily used system of weights and

measures universally acceptable to the countries of the world. These efforts were

motivated by two guiding principles. In the first place, there were many who hoped for

the definition of a single unit of measure that could serve as the basis for the logical

construction of a complete and consistent system of units of measure; in the second

place, there was also a growing number of people favoring decimal relationships for the

necessary units of the same quantity; that is, multiples by factors of ten or submultiples

by factors of one-tenth were considered to be the desirable means of obtaining

systematic units of measure that would be a convenient size for all needs.

The forces driving toward a change from diverse and essentially unrelated

customary systems of measure included rapidly growing international commerce and

the changing political structure of Europe and its colonial dependencies. Within the new

national structures it became necessary to accommodate many incompatible ways of

doing business. Moreover, the growth of scientific investigation not only created new

demands for accuracy and uniformity in measurements, it also provided the vision for a

universally acceptable scientific basis for a system of measurements. The customary

systems, handed down mainly from the Babylonians, Egyptians, Greeks, and Romans,

were based on unrelated objects and phenomena, including human anatomy, with no

practical hope for uniformity within integrated communities, states, or aggregated

nations.

WEEK 8

Origins of the Metric System

The birth of the metric system occurred in the climate of bold reform and

scientific rationalization that prevailed in France during the latter part of the 18th

century. In April 1790, Charles Maurice de Talleyrand, then Bishop of Autun, placed

before the National Assembly of France a plan based on a unit of length equal to the

length of a pendulum that would make one full swing per second. The French Academy

of Sciences organized special committees to study the related issues. While many

scientists favored the concept of a unit of length derived from a pendulum, there were

many recognized practical difficulties. These included variations with temperature and

the different values of gravitational force at different places on the surface of the Earth.

After scientific consideration of the alternatives, the committee recommended a new unit

of length equal to one ten-millionth of the length of the arc from the equator to the North

Pole, or a quadrant of the Earth's meridian circle. In May 1793 this unit was given the

name metre, derived from the Greek word metron, meaning "a measure." From the

same word came the name of the new system. The unit of mass, the kilogram, was

defined as the mass of water contained by a cube whose sides are one-tenth the unit of

length. The unit of volume, the liter, was defined in the same way; thus the unit of length

became the basis for the system. At that time the units of length, mass, area, volume,

and time satisfied the needs of commerce. The new Republic of France adopted the

recommendations of the French Academy in 1795.

Development of the System

The French Academy of Sciences also recommended, for practical reasons, that

the primary reference standard for the unit of length be realized from the definition of the

unit by a very precise measurement of the arc of meridian between Dunkirk, France,

and Barcelona, Spain. The length of the arc from the equator to the North Pole was then

to be inferred from astronomical measurements of angle. The survey was completed in

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November 1798, and platinum artifact reference standards for the meter and the

kilogram were constructed in June 1799. These two standards, deposited in the French

National Archives in Paris, later came to be known as the Meter of the Archives and the

Kilogram of the Archives.

The introduction of the metric system in France met with the usual resistance to

change. In 1812 the old units of measure were restored by Napoleon, Emperor of

France. In 1840 the metric system again became mandatory in France, and it has

remained so ever since. Meanwhile, the use of the metric system spread slowly to other

European countries and even to the United States, where it became legal, but not

mandatory, in 1866. The international acceptance of the metric system was

implemented by the Diplomatic Conference of the Meter, convened by the French

government on Mar. 1, 1875, and attended by delegates from 20 countries. This

conference produced the Treaty of the Meter, signed on May 20, 1875, by the delegates

of 17 countries--including the United States, the only English-speaking country to sign.

The metric treaty provided the institutional machinery needed to promote the

refinement, diffusion, and use of the metric system. The International Committee for

Weights and Measures, widely known as CIPM (Committee International des Poids et

Measures), was established under the broad supervision of the General Conference on

Weights and Measures, CGPM (Conference General des Poids et Measures),

consisting of delegates from member countries. The first General Conference met in

September 1889 to approve new international metric prototype reference standards to

redefine length and mass. These prototypes were based on the Archives standards.

The First CGPM also ratified the equality (within known uncertainties) of a number of

national prototype standards for length and mass and distributed these standards to the

member nations. This was the beginning of the diffusion of a uniform metric system

throughout the world. The Metric Convention also established the INTERNATIONAL

BUREAU OF WEIGHTS AND MEASURES, BIPM (Bureau International des Poids et

Mesures), to carry out the scientific work of the International System under the

supervision of CIPM.

WEEK 8

Metric expansion throughout the world

Following the reinstitution of the metric system in France in 1840, the use of the

system expanded slowly into parts of Germany, Italy, Greece, the Netherlands, and

Spain. After 1850 the growing interest in large international commercial exhibitions

accelerated the expansion of the use of the metric system as a common language of

measurements, and by 1880 the major European countries and most of South America

had adopted it. At the beginning of the 20th century the metric system was officially in

use in 35 countries, and the only large industrialized countries not included in that

number were the British Commonwealth countries and the United States. Both the

United States (in 1875) and Great Britain (in 1884) had become signatory nations of the

Treaty of the Meter, though, thereby recognizing the importance of a common

international basis for their national systems of measurement.

The metric displacement of customary measurement systems in major English-

speaking countries of the world has developed much more slowly. Changes in the

patterns of international trade and the importance of new markets in developing--as well

as developed-- countries has nevertheless brought about a practical regard for the

necessity of uniform units of measure on an international scale. The shift toward metric

conversion was well established in English- speaking countries by the middle of the

20th century. Official action to adopt the system for nationwide everyday use was finally

taken, after the establishment of the International System of Units in 1960, by Great

Britain (1965), South Africa (1968), New Zealand (1969), Canada (1970), and Australia

(1970). As the final quarter of the 20th century approaches, only the United States,

Liberia, and Burma remain uncommitted to the mandatory use of the metric system in

daily life.

WEEK 8

The Metric System in the United States

In the United States, there had been much official and scientific interest in the

development of the metric system during the earliest days of the nation. President

Washington urged Congress to take action toward uniform measurements throughout

the land. Thomas Jefferson and John Quincy Adams, during their terms as secretary of

state, carried out comprehensive studies that included consideration of the merits of the

metric system developments in France. Following an additional special study by the

newly organized National Academy of Sciences in January 1866, Congress enacted

legislation authorizing (but not mandating) the use of the metric system in the United

States. This legislation was signed into law by President Andrew Johnson on July 20,

1866.

The Act of 1866 was an important turning point in the history of measurements in

the United States. By making it lawful to employ weights and measures of the metric

system, the Act made a first step toward eventually harmonizing the U.S. measurement

system with those of other nations. The Act also defined by law the relationships to be

used in calculating the values of customary units of measurement used in the United

States from the corresponding metric units. Moreover, in that same year a joint

resolution authorized and directed the secretary of the treasury to furnish each state

with one set of standard metric weights and measures.

The United States was an important participant in the Convention of the meter

held in Paris in 1875. Following its signing of the Metric Convention on May 10, 1875,

the nation received its prototypes of the standard meter bar and standard kilogram in

1893. These became the nation's official fundamental standards for length and mass. In

1901 the U.S. NATIONAL BUREAU OF STANDARDS was established for the purpose

of serving the worlds of science and technology. Despite its efforts, little progress was

made toward a wider U.S. acceptance of metric units.

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Following World War II, however, and particularly following the USSR's

successful launching (1957) of the first space satellite, Sputnik--which opened the age

of space exploration--a renewed interest in the metric system developed in the United

States. By 1968 the spread of metric measurements throughout the world was nearly

complete. Arguments for conversion based on expanding foreign markets were

becoming increasingly persuasive. Recognizing these trends, Congress, on Aug. 9,

1968, authorized the secretary of commerce to undertake an intensive study to

determine the advantages and disadvantages of increased U. S. use of the metric

system. The resulting report, The U. S. Metric Study (1970-71), concluded that the

nation eventually would join the rest of the world in using the metric system and urged a

carefully planned transition to this use. On the recommendation of the study, Congress

enacted the Metric Conversion Act of 1975 and established the U. S. Metric Board "to

coordinate the voluntary conversion to the metric system." The Office of Metric

Programs then replaced the Metric Board in 1982.

Despite such efforts by the federal government, no states have as yet enacted

legislation mandating the adoption of International Units. Thus, popular use of the metric

system was still almost nonexistent by the early 1990s. The kind of pressure to adopt

the system that has a greater likelihood of success is instead coming from the business

community. Such pressure is being exerted in the cause of international competition

and trade. Organizations such as the European Economic Community, for example,

have threatened to restrict U.S. imports that do not conform to metric standards, and

some nations on occasion have already rejected shipments outright for such reasons.

Rather than trying to maintain dual inventories for domestic and foreign markets, a

number of U.S. corporations have chosen to go metric. (For example, motor vehicles,

farm machinery, and computer equipment are manufactured to metric specifications.)

As business goes, so probably will go the nation. The Omnibus Trade Bill, passed in

1988, has already required almost all federal agencies to use metric units in their

procurements, grants, and business activities by 1992.

WEEK 8

Base units and derived units

When the metric system was first conceived, one of the goals was the definition

of a single unit from which the essential system of measurements could be constructed.

Indeed, it was thought that the unit of length, the meter, should be regarded in this way,

and much scientific effort went into the careful selection of an acceptable definition. It

was also necessary to rely on the properties of pure water in order to define a unit of

mass, the kilogram. Thus, the measurement system required for trade and commerce in

the 18th century rested on the definitions of two units; units for other necessary

quantities, such as area and volume, were derived from them. The ultimate goal of a

complete system of measurements logically derived from the definition of a single unit

was not realizable when the metric system was first established, and it is not realizable

today. Nevertheless, the fundamental idea persisted, and a modern metric system has

been founded on six base units and designated by the 11th CGPM (1960) as the

International System of Units with the international abbreviation SI (see UNITS OF

MEASUREMENT). The SI base units--expanded to seven in 1971--are independent by

convention, and are the meter, kilogram, second, ampere, kelvin, mole, and candela. It

is possible, in principle, for industrial nations to maintain complete systems of

measurement that are equivalent within acceptable limits of uncertainty by comparing

national standards for the SI base units to those maintained by the International Bureau

of Weights and Measures, BIPM (Bureau International des Poids et Mesures), in

Sevres, France.

Future trends

The seven SI base units constitute a complete set in the sense that all the other

necessary units of measure can be logically derived from them. In a practical sense,

these seven also constitute an irreducible set within which no member can be derived

from any combination of the others. It is, however, possible that advances in science

and technology will result in a reduction of the number of SI base units. Since 1967 the

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SI unit for time, the second, has been defined as exactly 9,192,631,770 periods of radio

radiation emitted as a result of gyroscopic precession of the outermost electron in

undisturbed cesium atoms. From 1960 to 1983 the SI unit for length, the meter, was

defined as exactly 1,650,763.73 wavelengths of one of the spectral lines of krypton-86.

By 1983, however, even this laser-generated wavelength came to be considered

insufficiently accurate in reproducibility, and the meter was redefined as the length of

the path traveled by light in a vacuum during a time interval of 1/299,792,458 of a

second. That is, the standard unit of length is defined in terms of the speed of light.

Modern methods for the measurement of luminous energy provide another

example of advances that may, in principle, reduce the number of necessary SI base

units. The unit of luminous intensity, the candela, is defined in terms of the radiation

from a defined small area of a platinum body at a specified high temperature. It has

become possible to measure such radiation by direct comparison to equivalent small

amounts of electrical power. Therefore, electrical units--watts--are, in principle, sufficient

for the measurement of optical radiation flux, as well as of electrical power.

Recent advances using X rays to sense the positions of atoms in pure samples

of perfect crystalline structures have made it possible to determine the number of atoms

in a known amount of substance with great accuracy. On this basis, it may also become

practical to derive the SI mole directly from the kilogram, contributing thereby to further

simplification of the SI base units. Such advances even point the way to a possible

redefinition of the kilogram in terms of the mass of a selected universally available atom.

The present kilogram is the only SI base unit that is still defined in terms of an artifact

kept at Sevres.

In the case of special units in different disciplinary fields, it is clearly desirable to

encourage a trend toward uniform practice. For example, the units used to measure the

physiological effects of optical radiation include a factor for the average efficiency of the

human eye, while the corresponding units used in physics and engineering for the same

quantity do not. Similar examples exist in the case of other units that are used for

WEEK 8

physiological responses, including acoustic power and energy, and ionizing radiation

dose. Those who are concerned with the refinement of the modern metric system seek

ways to harmonize such diverse measurement practices while at the same time

avoiding any tendency to make the system less useful to those who have special needs.

The objective is to reduce the potential for confusion and error arising from the

limitations of measurement language used in widely different fields of scientific and

technological specialization.

WEEK 8

NAMES AND SYMBOLS FOR METRIC PREFIXES

Table 1

Prefix Symbol Multiplier

exa E 1,000,000,000,000,000,000

peta P 1,000,000,000,000,000

tera T 1,000,000,000,000

giga G 1,000,000,000

mega M 1,000,000

kilo k 1,000

hecto h 100

deka da 10

deci d 0.1centi c 0.01

milli m 0.001

nano u 001

atto n 0.000 000 001

pico p 0.000 000 000 001

femto f 0.000 000 000 000 001

micro a 0.000 000 000 000 000 001

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METRIC AND ENGLISH EQUIVALENTS

Table 2

Unit Metric English

acre 0.405 hectares 4,840 sq yardsbarrel (oil, US) 159 liters 42 gallons (US)

carat 200 milligrams .007 ounce avdp

degrees, C(Celsius)

water boils at 1000 deg. C

deg. C, freezes at

obtain degreesand add 32 tomultiply by 1.8

(Fahrenheit)degrees, F

subtract 32 and dividedegrees C

by 1.8 to obtain

water boils at 21at 32 deg. F

deg. F, freezesfoot 0.3048 meters 0.333 yards

gallon (US)         3.79 liters 4 quarts, liquid

hectare 0.1 sq kilometer 2.47 acres; 10,00 sq meters;

11,960 sq yardkilogram 0.001 tons, metric 2.2 pounds, avdp

hundredweight 45.36 kilograms 100 pounds, avdp

inch 2.54 centimeters 0.0278 yards

hectoliter 100 liters 26.42 gallons (US

hectoliter 100 liters 26.42 gallons (US

hundredweight 45.36 kilograms 100 pounds, avdp

inch 2.54 centimeters 0.0278 yards

kilogram 0.001 tons, metric 2.2 pounds, avdp

kilometer 1,000 meters 0.621 miles

kilometer, square 100 hectares 247 acres; 0.38sq miles

liter 0.01 hectoliter 1.06 quarts, liquid

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Meter 100 centimeters 1.09 yards

meter, square 1.196 sq yards -meter, cubic 1,000 liters 1.308 cu yards; 4

board feet

mile, nautical1.852 kilometers 1.151 miles

mile (statute)1.61 kilometers 5,280 feet

mile,square259 hectares 640 acres; 2.59 s

kilometerspound, avdp 0.454 kilograms 16 ounces, avdp

quart (US)0.946 liters 0.25 gallons (US)

ton, deadweight1.016 metric tons 2,240 pounds, avd

ton, long 1.016 metric tons 2,240 pounds, avd

ton, metric 1,000 kilograms 2,205 pounds, avdton, register 2.83 cu meters 100 cu feet

ton, short 0.907 metric tons 2,000 pounds, avd

yard 0.914 meters 3 feet

yard, square 0.836 sq meters 9 sq feet

yard, cubic 0.765 cu meters 27 cu feet

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Metric SystemAll living things are organized. This organization extends to all the measurable

parameters of a living structure (size, weight, surface area, and energy). Scientists use

a system of measure called the Metric System to record measurable parameters. The

objectives of this laboratory exercise are: to become more familiar with the rational for

using the Metric System, become proficient in the collection of biological information

using metric measurements, demonstrate an ability to convert between units of metric

measurement.

Rational

Why Metric? The metric system utilizes standard units derived from natural

systems. Other commonly used systems of measure e.g. english system use units that

often have no natural relevence to earth processes or a relationship between measured

units. In many cases the units were created based on the physical features associated

with a ruling monarch.

Exercise 1: Using the internet links provided below, answer the following

questions:

In the United States of America, we currently use the English system to assess

everyday measurements of length, weight, and temperature. 1) What are the standard

English units for these measurements? 2) Who is responsible for the creation of these

units? 3) What rational (if any) is behind the formulation of the unit?

Scientists use the Metric System of measure for everyday data collection. 1) What are

the standard metric units for length, mass, temperature, and volume? 2) What is the

rational behind each metric unit?

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Internet Resources

 National Institute of Standards and Technology

 Background on the SI

 Current definitions of the SI units

 Metric Internet Links

 METRIC STYLE GUIDE FOR

THE NEWS MEDIA

 NSTA: Scope, Sequence, and

Coordination

 Educational Resources  

 Pennsylvannia State University  Metric System

 Johnson County Community College The Metric System (Systeme

International)

 Colorado State Commonly used metric system

units, symbols, and prefixes

 Sam Houston State University  Ch.1: Metric System

 L. A. Pierce College  The Metric System

Conversions

Often the standardized unit for each kind of measurement is to large (or small) to

measure the intended object. We must use units of measure that are fractions or

multiples of the standard units. For example, if we measure a window using the english

system it might measure 23 3/4 inches. This measure uses both multiples and fractions

of the unit inches. The Metric System also allows for multiples or fractions of a unit to be

measured except that instead of using fractions with variable denominators the unit size

is variable. Unit size varies based on multiples of 10. The particular unit size to be

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measured is reflected in the prefix preceeding each unit measurement. The chart below

lists commonly used prefixes (in bold) and their reflective relationship to the

standardized unit of measure.

 Unit  Equivalent

 Kilometer (Km)  1000 meters

 Meter  1 meter

 decimeter (dm)  1/10 meter

 centimeter (cm)  1/100 meter

 millimeters (mm)  1/1,000 meter

 micrometer (um)  1/1,000,000 meter

 nanometers (nm)  1/1,000,000,000 meter

To directly compare data measurements, it may be necessary to convert all

measurements to a common unit value. In the example below, if we wish to compare

the height of two animals where the first animal was measured in centimeters and the

second animal was measured in millimeters we may wish to compare their height in

millimeters.

Animal 1) Height = 90 cm

Animal 2) Height = 45 mm

This would require us to convert the height of animal 1 from a value measured in

centimeter units into a value reflecting millimeter units.

To convert from one metric unit value to another requires two steps. Step 1: Ask

yourself, is the value I am converting to larger or smaller than the original unit size.

Using the example above: the measure of animal 1 height must be converted from

centimeter to millimeter units because we wish to compare height measurements in

millimeter units. Answer: millimeter units are smaller than centimeter units

(1mm=1/1000 m whereas 1cm=1/100 m).

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If the unit value you are converting to is smaller than the original unit value then a

multiplication function will be used.

If the unit value you are converting to is larger than the original unit value then a division

function will be used.

Let's use an example that is familiar to us: How many pennies are there in a

dollar bill? To convert our value from dollar to pennies we must multiply (the number of

pennies will exceed the number of dollars even though the total value of the transaction

remains the same).

Likewise, It is important to remember that when we are converting units from one

unit size to another unit size that the total value of the measurement remains the same

only the size of each unit has changed.

Step 2 requires us to know the difference in size between the units to be

converted. This "difference" between unit size will be the value that we will either

multiply or divide for the conversion. In the example above we are converting centimeter

unit into millimeter units. From the earlier chart we know that:

1 centimeter= 1/100m

1 millimeter = 1/1000m therefor 1 cm is 10 times greater in value than a millimeter.

"Difference" is 10.

If both values are expressed as fractions of the same reference (in this case "m")

then cancelling out the zeros can help expose the "difference between the unit values.

By cancelling zeros (multiplying each value by a common number) above we get:

1 centimeter = 1/100m x 100= 1/1 0r 1

1 millimeter = 1/1000m x 100=1/10 so a centimeter is 10 times larger than a

millimeter

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So to solve our original problem: What is the height of animal 1 in millimeters?

we do the following:

Step 1: the unit value we are converting to is smaller than the original unit value

so we will multiply (x).

Step 2: the "difference" between unit values is 10.

Answer: 90cm = __ mm is answered by 90x10 =900mm

The conversion format followed above works for any metric conversion you will

be asked to do reguardless of the unit of measure being collected. It is important that

you be able to recognize and undrstand the meaning behind the prefixes outlined

earlier.

Measurements

Most metric measurements are obtained using devices that you have been using to

collect English measurements.

Length

Metric length is collected with a ruler measured in meter (m), centimeter (cm), and/or

millimeter (mm) units. We use this instrument the same way we would use a foot ruler

or yard stick of the english system. Obtain a meter stick and centimeter ruler from the

supply table.

Locate the centimeter and millimeter markings.

How many centimeters are there in the meterstick?

How many millimeters are there in the meterstick? (Hint: count how many millimeters in

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1 centimeter)

How long is the centimeter ruler in cm? In mm?

Practice using the centimeter ruler or meter stick to measure objects around the room

(table, chair, classmates, shoe, pencil) until you are comfortable recording length in

metric units.

Practice converting your measurements from one unit value of length to another. Try

these. Use your centimeter ruler to assist if necessary.

10 cm = ___mm

25 mm = ___cm

95 cm = ___m

0.75m = ___cm = ___mm

5.5mm = ___m (tough one)

11.5cm = ___mm = ___m

Mass

Mass is measured in gram (g) units and is a measure of how much substance an object

consists of. Mass differs from weight because it is unaffected by gravity. The mass of an

astronaut on Earth or the moon is constant even though the weight of the astronaut is

less at the moon than on Earth. To measure mass we use a balance. Mass is calculated

with a balance similar to how an object might be weighed.

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Place an object in the pan of the balance. The arm of the balance is no longer

centered but rests above the center indication line. Using the counterbalances of known

mass (1g, 10g, or 100g), slide the counterbalances toward the right until the arm rests

at the centerline. If the arm falls below the centerline, move the counterbalance towards

the left. Practice balancing other objects from around the room.

Practice converting your measurements from one unit value of mass to another.

Try these practice problems.

150 mg=___g

1500g=___kg

950ug=___mg

2500ug=___g

1.5kg=___mg

Volume

Volume is a measured in liter (l) units and is a measure of how much space an object

occupies. Volume is a cubic measurement meaning that in order to calculate volume a

scientist needs to consider not only the length and width of an object but also the height.

Liquids and gases conform to the shape of the container they occupy. (Coffee poured

out of a pot conforms to the shape of the cup). To calculate the volume of a liquid a

scientist needs only to pour the solution that is being measured into a container of

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known volume. Scientists usually use a container called a graduated cylinder to

measure the volume of a liquid.