## metric system

**-**

## Metric System

# Metric System

Measuring units in folklore and history

Bigger and smaller metric units

Converting between English and metric units

The metric system is an internationally agreed-upon set of units for expressing the amounts of various quantities such as length, mass, time, temperature, and so on. It is used universally in science and almost so in daily life around the world.

Whenever we measure something, from the weight of a potato to the distance to the moon, we express the result as a number of specific units: for example, pounds or miles in the “English” system of measurement (still standard in the United States but no longer used extensively in England), or kilograms and kilometers in the metric system. As of 1994, every nation in the world had adopted some aspects of the metric system, with only four exceptions: the United States, Brunei, Burma, and Yemen.

The metric system that is in common use around the world is only a portion of the broader International System of Units, a comprehensive set of measuring units for almost every measurable physical quantity from the ordinary, such as time and distance, to the highly technical, such as the properties of energy, electricity and radiation. The International System of Units grew out of the 9th General [International] Conference on Weights and Measures, held in 1948. The 11th General Conference on Weights and Measures, held in 1960, refined the system and adopted the French name *Système International d’Unite´s,* abbreviated SI.

Because of its convenience and consistency, scientists have used the metric system of units for more than 200 years. Originally, the metric system was based on only three fundamental units: the meter for length, the kilogram for mass, and the second for time. Today, there are more than 50 officially recognized SI units for various scientific quantities.

## Measuring units in folklore and history

In the biblical story of Noah, the ark was supposed to be 300 cubits long and 30 cubits high. Like all early units of size, the cubit was based on the always-handy human body, and was most likely the length of a man’s forearm from elbow to fingertip. You could measure a board, for example, by laying your forearm down successively along its length. In the Middle Ages, the inch is reputed to have been the length of a medieval king’s first thumb joint. The yard was once defined as the distance between the nose of England’s King Henry I and the tip of his outstretched middle finger. The origin of the foot as a unit of measurement is obvious.

In Renaissance Italy, Leonardo da Vinci used what he called a *braccio,* or arm, in laying out his works. It was equal to two *palmi,* or palms. But arms and palms, of course, will differ. In Florence, the engineers used a *braccio* that was 23 inches long, while the surveyors’ *braccio* averaged only 21.7 inches. The foot, or *piede,* was about 17 inches in Milan, but only about 12 inches in Rome.

Eventually, ancient “rule of thumb” gave way to more carefully defined units. The metric system was adopted in France in 1799 and the British Imperial System of units was established in 1824. In 1893, the English units used in the United States were redefined in terms of their metric equivalents: the yard was defined as 0.9144 meter, and so on. But English units continue to be used in the United States to this day, even though the Omnibus Trade and Competitiveness Act of 1988 stated that “it is the declared policy of the United States. . .to designate the metric system of measurement as the preferred system of weights and measures for United States trade and commerce.”

English units are based on inconsistent standards. When that medieval king’s thumb became regrettably unavailable for further consultation, the standard for the inch was changed to the length of three grains of barley, placed end to end—not much of an improvement. Metric units, on the other hand, are based on defined and controlled standards, not on the whims of humans.

The standards behind the English units are not reproducible. Arms, hands, and grains of barley will obviously vary in size; the size of a 3-foot yard depends on whose feet are in question. But metric units are based on standards that are precisely reproducible, time after time.

There are many English units, including buckets, butts, chains, cords, drams, ells, fathoms, firkins, gills, grains, hands, knots, leagues, three different kinds of miles, four kinds of ounces, and five kinds of tons, to name just a few. There are literally hundreds more. For measuring volume or bulk alone, the English system uses ounces, pints, quarts, gallons, barrels and bushels, among many others. In the metric system, on the other hand, there is only one basic unit for each type of quantity.

Any measuring unit, in whatever system, will be too big for some applications and too large for others. To express all distances in miles and all weight in ounces, for example, would require the constant use of very small or very large numbers, with consequent waste of time in recording and communicating those numbers. That is why we have inches and tons as well as miles and ounces. The problem, though, is that in the American (“English”) system the conversion factors between various-sized units—12 inches per foot, 3 feet per yard, 1,760 yards per mile. They’re completely arbitrary. Metric units, on the other hand, have conversion factors that are all powers of ten. That is, the metric system is a decimal system, just like dollars and cents. In fact, the entire system of numbers is decimal, based on tens, not threes or twelves. Therefore, converting a unit from one size to another in the metric system is just a matter of moving the decimal point.

## The metric units

The SI starts by defining seven basic units: one each for length, mass, time, electric current, temperature, amount of substance and luminous intensity. (“Amount of substance” refers to the number of elementary particles in a sample of matter. Luminous intensity has to do with the brightness of a light source.) But only four of these seven basic quantities are in everyday use by non-scientists: length, mass, time, and temperature. Their defined SI units are the meter for length, the kilogram for mass, the second for time and the degree Celsius for temperature. (The other three basic units are the ampere for electric current, the mole for amount of substance, and the candela for luminous intensity.) Almost all other units can be derived from the basic seven. For example, area is a product of two lengths: meters squared, or square meters. Velocity or speed is a combination of a length and a time: kilometers per hour.

The meter was originally defined in terms of Earth’s size; it was supposed to be one ten-millionth of the distance from the equator to the North Pole, going straight through Paris. The modern meter, however, is defined in terms of how far light will travel in a given amount of time when traveling at—naturally— the speed of light. The speed of light in a vacuum is considered to be a fundamental constant of nature that is invariable, no matter how the continents drift. The standard meter turns out to be 39.3701 inches.

The kilogram is the metric unit of mass, not weight. Mass is the fundamental measure of the amount of matter in an object. The mass of a baseball won’t change if you hit it from Earth to the moon, but it will weigh less—have less weight—when it lands on the moon because the moon’s smaller gravitational force is pulling it down less strongly. Astronauts can be weightless in space, but they can lose mass only by dieting. As long as we don’t leave Earth, though, we can speak loosely about mass and weight as if they were the same thing. So you can feel free to “weigh” yourself (not “mass” yourself) in kilograms. Unfortunately, no absolutely unchangeable standard of mass has yet been found to standardize the kilogram on Earth. The kilogram is therefore defined as the mass of a certain bar of platinum-iridium alloy that has been kept (very carefully) since 1889 at the International Bureau of Weights and Measures in Sèvres, France. The kilogram turns out to be 2.2046 pounds.

The metric unit of time is the same second that has always been used, except that it is now defined in a more precise way. It no longer depends on the wobbly rotation of Earth (1/86,400th of a day), because the planet is slowing down; days keep getting a little longer as its rotation slows. So the second is now defined in terms of the vibrations of a certain kind of atom known as cesium-133. One second is defined as the

amount of time it takes for a cesium-133 atom to vibrate in a particular way 9,192,631,770 times. This may sound like a strange definition, but it is a superbly accurate way of fixing the standard size of the second, because the vibrations of atoms depend only on the nature of the atoms themselves, and cesium atoms will presumably continue to behave exactly like cesium atoms forever. The exact number of cesium vibrations was chosen to come out as close as possible to what was previously the most accurate value of the second.

The metric unit of temperature is the degree Celsius (^{o}C), which replaces the English system’s degree Fahrenheit (^{°}F). In the scientists’ SI, the fundamental unit of temperature is actually the kelvin (K)—not the “degree Kelvin,” simply the Kelvin. The kelvin and the degree Celsius are exactly the same size, namely, 1.8 times as large as the degree Fahrenheit. One cannot convert between the Celsius or Kelvin scales and Fahrenheit simply by multiplying or dividing by 1.8, however, because the scales start at different places. That is, their zero-degree marks have been set at different temperatures. This is also true of the Kelvin and Celsius scales, though there the conversion is quite easy: the temperature in Kelvins is the temperature in degrees Celsius minus 273.15. Zero degrees Kelvin is absolute zero, the lowest possible temperature—no molecular motion at all (or, strictly speaking, as close to that state as quantum mechanics permits).

## Bigger and smaller metric units

Because the meter (1.0936 yards) is much too big for measuring an atom and much too small for measuring the distance between two cities, we need a variety of smaller and larger units of length. But instead of

### KEY TERMS

**Kelvin—** The International System (SI) unit of temperature. It is the same size as the degree Celsius.

**Mass—** A measure of the amount of matter in a sample of any substance. Mass does not depend on the strength of a planet’s gravitational force, as does weight.

**Matter—** Any substance. Matter has mass and occupies space.

**Temperature—** A measure of the average kinetic energy of all the elementary particles in a sample of matter.

inventing different-sized units with completely different names, as the English-American system does, we can create a metric unit of almost any desired size by attaching a prefix to the name of the unit. For example, since kilo- is a Greek form meaning a thousand, a kilometer (kil-OM-et-er) is a thousand meters. Similarly, a kilogram is a thousand grams; a gigagram is a billion grams or 10^{9} grams; and a nanosecond is one billionth of a second or 10^{-9} second.

Minutes are permitted to remain in the metric system for convenience or for historical reasons, even though they don’t conform strictly to the rules. The minute, hour, and day, for example, are so customary that they’re still defined in the metric system as 60 seconds, 60 minutes, and 24 hours—not as multiples of ten. For volume, the most common metric unit is not the cubic meter, which is generally too big to be useful in commerce, but the liter, which is one thousandth of a cubic meter. For even smaller volumes, the milliliter, one thousandth of a liter, is commonly used. And for large masses, the metric ton is often used instead of the kilogram. A metric ton (often spelled tonne in other countries) is 1,000 kilograms. Because a kilogram is about 2.2 pounds, a metric ton is about 2,200 pounds: 10% heavier than an American ton of 2,000 pounds. Another often-used, non-standard metric unit is the hectare for land area. A hectare is 10,000 square meters and is equivalent to 0.4047 acre.

## Converting between English and metric units

The problem of changing over a highly industrialized nation such as the United States to a new system of measurements is substantial. Once the metric system is in general use in the United States, its simplicity and convenience will be enjoyed, but the transition period, when both systems are in use, can be difficult. However, there are only a small number of SI units and prefixes that are used in everyday life and to which the average person would have to become accustomed.

*See also* Units and standards.

## Resources

### BOOKS

*Alder, Ken. The Measure of All Things: The Seven Year Odyssey and Hidden Error that Transformed the World.* New York: Free Press, 2002.

Fandel, Jennifer. *The Metric System (What in the World?).* Hadley, MA: Creative Education, 2006.

Hebra, Alexius J. *Measure for Measure: The Story of Imperial, Metric, and Other Units.* Baltimore: Johns Hopkins University Press, 2003.

Robert L. Wolke

## Metric System

# Metric system

The metric system of measurement is an internationally agreed-upon set of units for expressing the amounts of various quantities such as length, mass, time, and temperature. As of 1994, every nation in the world has adopted the metric system, with only four exceptions: the United States, Brunei, Burma, and Yemen (which use the English units of measurement).

Because of its convenience and consistency, scientists have used the metric system of units for more than 200 years. Originally, the metric system was based on only three fundamental units: the meter for length, the kilogram for mass, and the second for time. Today, there are more than 50 officially recognized units for various scientific quantities.

## Measuring units in folklore and history

Nearly all early units of size were based on the always-handy human body. In the Middle Ages, the inch is reputed to have been the length of a medieval king's first thumb joint. The yard was once defined as the distance between English king Henry I's nose and the tip of his outstretched middle finger. The origin of the foot as a unit of measurement is obvious.

Eventually, ancient "rules of thumb" gave way to more carefully defined units. The metric system was adopted in France in 1799.

## The metric units

The metric system defines seven basic units: one each for length, mass, time, electric current, temperature, amount of substance, and luminous intensity. (Amount of substance refers to the number of elementary particles in a sample of matter; luminous intensity has to do with the brightness of a light source.) But only four of these seven basic quantities are in everyday use by nonscientists: length, mass, time, and temperature. Their defined units are the meter for length, the kilogram for mass, the second for time, and the degree Celsius for temperature. (The other three basic units are the ampere for electric current, the mole for amount of substance, and the candela for luminous intensity.)

The meter was originally defined in terms of Earth's size; it was supposed to be one ten-millionth of the distance from the equator to the North Pole. Since Earth is subject to geological movements, this distance does not remain the same. The modern meter, therefore, is defined in terms of how far light will travel in a given amount of time when traveling at the speed of light. The speed of light in a vacuum—186,282 miles (299,727 kilometers) per hour—is considered to be a fundamental constant of nature that will never change. The standard meter is equivalent to 39.3701 inches.

The kilogram is the metric unit of mass, not weight. Mass is the fundamental measure of the amount of matter in an object. Unfortunately, no absolutely unchangeable standard of mass has yet been found on which to standardize the kilogram. The kilogram is therefore defined as the mass of a certain bar of platinum-iridium alloy that has been kept since 1889 at the International Bureau of Weights and Measures in Sèvres, France. The kilogram is equivalent to 2.2046 pounds.

## Metric System

### MASS AND WEIGHT

Unit |
Abbreviation |
Mass of Grams |
U.S. Equivalent (approximate) |

metric ton | t | 1,000,000 | 1.102 short tons |

kilogram | kg | 1,000 | 2.2046 pounds |

hectogram | hg | 100 | 3.527 ounces |

dekagram | dag | 10 | 0.353 ounce |

gram | g | 1 | 0.035 ounce |

decigram | dg | 0.1 | 1.543 grains |

centigram | cg | 0.01 | 0.154 grain |

milligram | mg | 0.001 | 0.015 grain |

microgram | μm | 0.000001 | 0.000015 grain |

### LENGTH

Unit |
Abbreviation |
Mass of Grams |
U.S. Equivalent (approximate) |

kilometer | km | 1,000 | 0.62 mile |

hectometer | hm | 100 | 328.08 feet |

dekameter | dam | 10 | 32.81 feet |

meter | m | 1 | 39.37 inches |

decimeter | dm | 0.1 | 3.94 inches |

centimeter | cm | 0.01 | 0.39 inch |

millimeter | mm | 0.001 | 0.039 inch |

micrometer | μm | 0.000001 | 0.000039 inch |

### AREA

Unit |
Abbreviation |
Mass of Grams |
U.S. Equivalent (approximate) |

square kilometer | sq km or km^{2} |
1,000,000 | 0.3861 square miles |

hectare | ha | 10,000 | 2.47 acres |

are | a | 100 | 119.60 square yards |

square centimeter | sq cm or cm^{2} |
0.0001 | 0.155 square inch |

### VOLUME

Unit |
Abbreviation |
Mass of Grams |
U.S. Equivalent (approximate) |

cubic meter | m^{3} |
1 | 1.307 cubic yards |

cubic decimeter | dm^{3} |
0.001 | 61.023 cubic inches |

cubic centimeter | cu cm or cm^{3} or cc |
0.000001 | 0.061 cubic inch |

### CAPACITY

Unit |
Abbreviation |
Mass of Grams |
U.S. Equivalent (approximate) |

kiloliter | kl | 1,000 | 1.31 cubic yards |

hectoliter | hl | 100 | 3.53 cubic feet |

dekaliter | dal | 10 | 0.35 cubic foot |

liter | l | 1 | 61.02 cubic inches |

cubic decimeter | dm^{3} |
1 | 61.02 cubic inches |

deciliter | dl | 0.10 | 6.1 cubic inches |

centiliter | cl | 0.01 | 0.61 cubic inch |

milliliter | ml | 0.001 | 0.061 cubic inch |

microliter | μl | 0.000001 | 0.000061 cubic inch |

The metric unit of time is the same second that has always been used, except that it is now defined in a very accurate way. It no longer depends on the wobbly rotation of our planet (1/86,400th of a day), because Earth is slowing down. Days keep getting a little longer as Earth grows older. So the second is now defined in terms of the vibrations of a certain kind of atom known as cesium-133. One second is defined as the amount of time it takes for a cesium-133 atom to vibrate in a particular way 9,192,631,770 times. Because the vibrations of atoms depend only on the nature of the atoms themselves, cesium atoms will presumably continue to behave exactly like cesium atoms forever. The exact number of cesium vibrations was chosen to come out as close as possible to what was previously the most accurate value of the second.

The metric unit of temperature is the degree Celsius, which replaces the English system's degree Fahrenheit. It is impossible to convert between Celsius and Fahrenheit simply by multiplying or dividing by 1.8, however, because the scales start at different places. That is, their zero-degree marks have been set at different temperatures.

## Bigger and smaller metric units

In the metric system, there is only one basic unit for each type of quantity. Smaller and larger units of those quantities are all based on powers of ten (unlike the English system that invents different-sized units with completely different names based on different conversion factors: 3, 12, 1760, etc.). To create those various units, the metric system simply attaches a prefix to the name of the unit. Latin prefixes are added for smaller units, and Greek prefixes are added for larger units. The basic prefixes are: kilo- (1000), hecto- (100), deka- (10), deci- (0.1), centi- (0.01), and milli- (0.001). Therefore, a kilometer is 1,000 meters. Similarly, a millimeter is one-thousandth of a meter.

Minutes are permitted to remain in the metric system even though they don't conform strictly to the rules. The minute, hour, and day, for example, are so customary that they're still defined in the metric system as 60 seconds, 60 minutes, and 24 hours—not as multiples of ten. For volume, the most common metric unit is not the cubic meter, which is generally too big to be useful in commerce, but the liter, which is one-thousandth of a cubic meter. For even smaller volumes, the milliliter, one-thousandth of a liter, is commonly used. And for large masses, the metric ton is often used instead of the kilogram. A metric ton (often spelled tonne) is 1,000 kilograms. Because a kilogram is about 2.2 pounds, a metric ton is about 2,200 pounds: 10 percent heavier than an American ton of 2,000 pounds. Another often-used, nonstandard metric unit is the hectare for land area. A hectare is 10,000 square meters and is equivalent to 0.4047 acre.

[*See also* **Units and standards** ]

## Metric System

# Metric system

The metric system of measurement is an internationally agreed-upon set of units for expressing the amounts of various quantities such as length, mass, **time** , **temperature** , and so on.

Whenever we measure something, from the weight of a sack of potatoes to the distance to the **moon** , we must express the result as a number of specific units: for example, pounds and miles in the English system of measurement (although even England no longer fully uses that system), or kilograms and kilometers in the metric system. As of 1994, every nation in the world had adopted some aspects of the metric system, with only four exceptions: the United States, Brunei, Burma, and Yemen.

The metric system that is in common use around the world is only a portion of the broader International System of Units, a comprehensive set of measuring units for almost every measurable physical quantity from the ordinary, such as time and distance, to the highly technical, such as the properties of **energy** , **electricity** and **radiation** . The International System of Units grew out of the 9th General [International] Conference on Weights and Measures, held in 1948. The 11th General Conference on Weights and Measures, held in 1960, refined the system and adopted the French name *Système International d'Unités*, abbreviated as SI.

Because of its convenience and consistency, scientists have used the metric system of units for more than 200 years. Originally, the metric system was based on only three fundamental units: the meter for length, the kilogram for mass, and the second for time. Today, there are more than 50 officially recognized SI units for various scientific quantities.

## Measuring units in folklore and history

In the biblical story of Noah, the ark was supposed to be 300 cubits long and 30 cubits high. Like all early units of size, the cubit was based on the always-handy human body, and was most likely the length of a man's forearm from elbow to fingertip. You could measure a board, for example, by laying your forearm down successively along its length. In the Middle Ages, the inch is reputed to have been the length of a medieval king's first thumb joint. The yard was once defined as the distance between the nose of England's King Henry I and the tip of his outstretched middle finger. The origin of the foot as a unit of measurement is obvious.

In Renaissance Italy, Leonardo da Vinci used what he called a *braccio*, or arm, in laying out his works. It was equal to two *palmi*, or **palms** . But arms and palms, of course, will differ. In Florence, the engineers used a *braccio* that was 23 inches long, while the surveyors' *braccio* averaged only 21.7 inches. The foot, or *piede*, was about 17 inches in Milan, but only about 12 inches in Rome.

Eventually, ancient "rules of thumb" gave way to more carefully defined units. The metric system was adopted in France in 1799 and the British Imperial System of units was established in 1824. In 1893, the English units used in the United States were redefined in terms of their metric equivalents: the yard was defined as 0.9144 meter, and so on. But English units continue to be used in the United States to this day, even though the Omnibus Trade and Competitiveness Act of 1988 stated that "it is the declared policy of the United States...to designate the metric system of measurement as the preferred system of weights and measures for United States trade and commerce."

English units are based on inconsistent standards. When that medieval king's thumb became regrettably unavailable for further consultation, the standard for the inch was changed to the length of three grains of **barley** , placed end to end—not much of an improvement. Metric units, on the other hand, are based on defined and controlled standards, not on the whims of humans.

The standards behind the English units are not reproducible. Arms, hands, and grains of barley will obviously vary in size; the size of a 3-foot yard depends on whose feet are in question. But metric units are based on standards that are precisely reproducible, time after time.

There are many English units, including buckets, butts, chains, cords, drams, ells, fathoms, firkins, gills, grains, hands, knots, leagues, three different kinds of miles, four kinds of ounces, and five kinds of tons, to name just a few. There are literally hundreds more. For measuring **volume** or bulk alone, the English system uses ounces, pints, quarts, gallons, barrels and bushels, among many others. In the metric system, on the other hand, there is only one basic unit for each type of quantity.

Any measuring unit, in whatever system, will be too big for some applications and too large for others. People would not appreciate having their waist measurements in miles or their weights in tons. That's why we have inches and pounds. The problem, though, is that in the American system the conversion factors between various-sized units—12 inches per foot, 3 feet per yard, 1,760 yards per mile. They're completely arbitrary. Metric units, on the other hand, have conversion factors that are all powers of ten. That is, the metric system is a decimal system, just like dollars and cents. In fact, the entire system of numbers is decimal, based on tens, not threes or twelves. Therefore, converting a unit from one size to another in the metric system is just a matter of moving the decimal point.

## The metric units

The SI starts by defining seven basic units: one each for length, mass, time, **electric current** , temperature, amount of substance and luminous intensity. ("Amount of substance" refers to the number of elementary particles in a sample of matter. Luminous intensity has to do with the brightness of a **light** source.) But only four of these seven basic quantities are in everyday use by nonscientists: length, mass, time, and temperature. Their defined SI units are the meter for length, the kilogram for mass, the second for time and the degree Celsius for temperature. (The other three basic units are the ampere for electric current, the **mole** for amount of substance, and the candela for luminous intensity.) Almost all other units can be derived from the basic seven. For example, area is a product of two lengths: meters squared, or square meters. **Velocity** or speed is a combination of a length and a time: kilometers per hour.

The meter was originally defined in terms of Earth's size; it was supposed to be one ten-millionth of the distance from the equator to the North Pole, going straight through Paris. The modern meter, therefore, is defined in terms of how far light will travel in a given amount of time when traveling at—naturally—the speed of light. The speed of light in a **vacuum** is considered to be a fundamental constant of nature that is invariable, no matter how the continents drift. The standard meter turns out to be 39.3701 inches.

The kilogram is the metric unit of mass, not weight. Mass is the fundamental measure of the amount of matter in an object. The mass of a baseball won't change if you hit it from the earth to the moon, but it will weigh less—have less weight—when it lands on the moon because the moon's smaller gravitational **force** is pulling it down less strongly. Astronauts can be weightless in **space** , but they can lose mass only by dieting. As long as we don't leave the earth, though, we can speak loosely about mass and weight as if they were the same thing. So you can feel free to "weigh" yourself (not "mass" yourself) in kilograms. Unfortunately, no absolutely unchangeable standard of mass has yet been found to standardize the kilogram on Earth. The kilogram is therefore defined as the mass of a certain bar of platinum-iridium **alloy** that has been kept (very carefully) since 1889 at the International
Bureau of Weights and Measures in Sèvres, France. The kilogram turns out to be 2.2046 pounds.

The metric unit of time is the same second that has always been used, except that it is now defined in a more precise way. It no longer depends on the wobbly **rotation** of Earth (1/86,400th of a day), because Earth is slowing down; her days keep getting a little longer as rotation slows. So the second is now defined in terms of the vibrations of a certain kind of atom known as cesium-133. One second is defined as the amount of time it takes for a cesium-133 atom to vibrate in a particular way 9,192,631,770 times. This may sound like a strange definition, but it is a superbly accurate way of fixing the standard size of the second, because the vibrations of **atoms** depend only on the nature of the atoms themselves, and cesium atoms will presumably continue to behave exactly like cesium atoms forever. The exact number of cesium vibrations was chosen to come out as close as possible to what was previously the most accurate value of the second.

The metric unit of temperature is the degree Celsius (oC), which replaces the English system's degree Fahrenheit (oF). In the scientists' SI, the fundamental unit of temperature is actually the kelvin (K). But the kelvin and the degree Celsius are exactly the same size: 1.8 times as large as the degree Fahrenheit. One cannot convert between Celsius and Fahrenheit simply by multiplying or dividing by 1.8, however, because the scales start at different places. That is, their zero-degree marks have been set at different temperatures.

## Bigger and smaller metric units

Because the meter (1.0936 yards) is much too big for measuring an atom and much too small for measuring the distance between two cities, we need a variety of smaller and larger units of length. But instead of inventing different-sized units with completely different names, as the English-American system does, we can create a metric unit of almost any desired size by attaching a prefix to the name of the unit. For example, since kilo- is a Greek form meaning a thousand, a kilometer (kil-OM-et-er) is a thousand meters. Similarly, a kilogram is a thousand grams; a gigagram is a billion grams or 109 grams; and a nanosecond is one billionth of a second or 10-9 second.

Minutes are permitted to remain in the metric system for convenience or for historical reasons, even though they don't conform strictly to the rules. The minute, hour, and day, for example, are so customary that they're still defined in the metric system as 60 seconds, 60 minutes, and 24 hours—not as multiples of ten. For volume, the most common metric unit is not the cubic meter, which is generally too big to be useful in commerce, but the liter, which is one thousandth of a cubic meter. For even smaller volumes, the milliliter, one thousandth of a liter, is commonly used. And for large masses, the metric ton is often used instead of the kilogram. A metric ton (often spelled tonne in other countries) is 1,000 kilograms. Because a kilogram is about 2.2 pounds, a metric ton is about 2,200 pounds: 10% heavier than an American ton of 2,000 pounds. Another often-used, non-standard metric unit is the hectare for land area. A hectare is 10,000 square meters and is equivalent to 0.4047 acre.

## Converting between English and metric units

The problem of changing over a highly industrialized nation such as the United States to a new system of measurements is a substantial one. Once the metric system is in general use in the United States, its simplicity and convenience will be enjoyed, but the transition period, when both systems are in use, can be difficult. Nevertheless, it will be easier than it seems. While the complete SI is intimidating because it covers every conceivable kind of scientific measurement over an enormous range of magnitudes, there are only a small number of units and prefixes that are used in everyday life.

See also Units and standards.

## Resources

### books

Alder, Ken. *The Measure of All Things: The Seven Year Odyssey and Hidden Error that Transformed the World.* New York: Free Press, 2002.

Hebra, Alexius J. *Measure for Measure: The Story of Imperial, Metric, and Other Units.* Baltimore: Johns Hopkins University Press, 2003.

### periodicals

"The International System of Units (SI)." *United States Department of Commerce, National Institute of Standards and Technology, Special Publication* 330 (1991).

### other

Bartlett, David. *A Concise Reference Guide to the Metric System* [cited October 2002]. <http://www.bms.abdn.ac.uk/undergraduate/guidetounits.html>.

"Interpretation of the SI for the United States and Metric Conversion Policy for Federal Agencies." *United States Department of Commerce, National Institute of Standards and Technology, Special Publication* 814 (1991).

Robert L. Wolke

## KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .**Kelvin**—The International System (SI) unit of temperature. It is the same size as the degree Celsius.

**Mass**—A measure of the amount of matter in a sample of any substance. Mass does not depend on the strength of a planet's gravitational force, as does weight.

**Matter**—Any substance. Matter has mass and occupies space.

**Temperature**—A measure of the average kinetic energy of all the elementary particles in a sample of matter.

## metric system

metric system, system of weights and measures planned in France and adopted there in 1799; it has since been adopted by most of the technologically developed countries of the world. It is based on a unit of length, called the meter (m), and a unit of mass, called the kilogram (kg).

The system has changed somewhat since it was first developed; e.g., the definition of the meter has changed, and the unit for mass is different. The meter was originally intended to be 1/10,000,000 of the distance on the earth's surface between the equator and either pole; however, because of errors in the original survey for determining the meter and because of the impracticality of referring to such a standard, the meter was later redefined in terms of the standard prepared and kept at Sèvres, France, near Paris. Long defined as the distance between two scratches on a bar of platinum-iridium alloy, the meter in 1960 was first redefined in terms of an atomic standard. In 1983 the meter was officially redefined as the distance traveled by light in vacuum during 1/299,792,458 of a second.

The original unit of mass, the gram, was first defined as the mass of pure water at maximum density that would fill a cube whose edges are each 0.01 m. The unit of mass is now the kilogram, defined as the mass of a platinum-iridium cylinder kept at Sèvres. (A gram is now defined as a mass 1/1,000 kg.) Other metric units can be defined in terms of the meter and the kilogram. For example the are, the unit of area, is equal to the area of a square whose edges are each 10 m long. The liter, the metric unit of volume, is equal to the volume of a cube whose edges are each 1/10 m long.

Fractions and multiples of the metric units are related to each other by powers of 10, allowing conversion from one unit to a multiple of it simply by shifting a decimal point, and avoiding the lengthy arithmetical operations required by the English units of measurement. Standard prefixes (found in the table entitled Prefixes for Basic Metric Units) have been accepted for designating multiples and fractions of the meter, gram, are, and other units. Thus, 1,000 grams are a kilogram, 100 ares are a hectare, and 1/100 of a meter is a centimeter.

Several other systems of units based on the metric system have been in wide use. The cgs system is based on the centimeter of length, the gram of mass, and the second of time. The mks system is based on the meter of length, the kilogram of mass, and the second of time. Units in the mks system are larger than the corresponding cgs units. Electric and magnetic units have been defined for both of these systems; in fact, two different sets of electric units are defined in the cgs system. The mks system serves as the basis for the International System of Units, a comprehensive system of units for all physical quantities adopted in 1960 by the 11th General Conference on Weights and Measures.

See also decimal system.

See L. V. Judson, *Weights and Measures Standards of the United States: A Brief History* (1976; U.S. National Bureau of Standards Special Publication 447); K. Alder, *The Measure of All Things* (2002).

## metric system

**metric system** Decimal system of weights and measures based on the metre (m) and the kilogram (kg). Larger and smaller metric units relate by powers of 10. Devised in 1791, the metric system is used internationally by scientists (particularly as SI units) and has been adopted for general use by most Western countries, although the imperial system is still commonly used in the USA and for certain measurements in Britain.

## metric system

met·ric sys·tem • n. the decimal measuring system based on the meter, liter, and gram as units of length, capacity, and weight or mass. The system was first proposed by the French astronomer and mathematician Gabriel Mouton (1618–94) in 1670 and was standardized in France under the Republican government in the 1790s.