## Units and Standards

## Units and Standards

# Units and Standards

Le Système International d’Unités (the SI system)

Unit conversions between systems

A unit of measurement is some specific quantity that has been chosen as the standard against which other measurements of the same kind are made. For example, the meter (m) is the unit of measurement for length in the metric system. When an object is said to be 4 m long, that means that the object is four times as long as the unit standard (1 m).

The term standard refers to the physical object on which the unit of measurement is based. For example, for many years the standard used in measuring length in the metric system was the distance between two scratches on a platinum-iridium bar kept at the Bureau of Standards in Sèvres, France. A standard serves as a model against which other measuring devices of the same kind are made. The meter stick in a classroom or home is thought to be exactly 1 m long because it was made from a permanent model kept at the manufacturing plant that was originally copied from the standard meter in France.

All measurements consist of two parts: a scalar (numerical) quantity and the unit designation. In the measurement 8.5 m, the scalar quantity is 8.5 and the unit designation is meters.

## History

the need for units and standards developed at a point in human history when people needed to know how much of something they were buying, selling, or exchanging. A farmer might want to sell a bushel of wheat, for example, for 10 dollars, but he or she could do so only if the unit bushel was known to potential buyers. Furthermore, the unit bushel had to have the same meaning for everyone who used the term.

The measuring system that most Americans know best is the British system, with units including the foot, yard, second, pound, and gallon. The British system grew up informally and in a disorganized way over many centuries. The first units of measurement probably came into use shortly after 1215. These units were tied to easily obtained or produced standards. The yard, for example, was defined as the distance from King Henry II’s nose to the thumb of his outstretched hand.

The British system of measurement consists of a complex, irrational collection of units whose only advantage is its familiarity. As an example of the problems it poses, the British system has three different units known as the quart. These are the British quart, the United States dry quart, and the United States liquid quart. The exact size of each of these quarts differs.

In addition, a number of different units are in use for specific purposes. Among the units of volume in use in the British system, (in addition to those mentioned above) are the bag, barrel (of which there are three types—British and United States dry, United States liquid, and United States petroleum), bushel, butt, cord, drachm, firkin, gill, hogshead, kilderkin, last, noggin, peck, perch, pint, and quarter.

## The metric system

In an effort to bring some rationality to systems of measurement, the French National Assembly established a committee in 1790 to propose a new system of measurement, with new units and new standards. That system has come to be known as the metric system and is now the only system of measurement used by all scientists and in every country of the world except the United States, Liberia (in western Africa) and the Myanmar Republic (formerly known as Burma, in Southeast Asia). The units of measurement chosen for the metric system were the gram (abbreviated g) for mass, the liter (l) for volume, the meter (m) for length, and the second (s) for time.

A specific standard was chosen for each of these basic units. The meter was originally defined as one ten-millionth the distance from the north pole (on the Earth) to the equator along the prime meridian. As a definition, this standard is perfectly acceptable, but it has one major disadvantage: a person who wants to make a meter stick would have difficulty using that standard to construct a meter stick of his or her own.

As a result, new and more suitable standards were selected over time. One improvement was to construct the platinum-iridium bar standard mentioned above. Manufacturers of measuring devices could ask for copies of the fundamental standard kept in France and then make their own copies from those. As one can imagine, the more copies of copies that had to be made, the less accurate the final measuring device would be.

The most recent standard adopted for the meter solves this problem. In 1983, the international Conference on Weights and Measures defined the meter as the distance that light travels (in vacuum) in 1/299,792,458 second. The standard is useful because it depends on the most accurate physical measurement known—the second—and because anyone in the world is able, given the proper equipment, to determine the true length of a meter.

## Le Système International d’Unités (the SI system)

In 1960, the metric system was modified somewhat with the adoption of new units of measurement. The modification was given the name of Le Système International d’Uniteś, or the International System of Units—more commonly known as the SI system.

Nine fundamental units make up the SI system. These are the meter (abbreviated m) for length, the kilogram (kg) for mass, the second (s) for time, the ampere (A) for electric current, the Kelvin (K) for temperature, the candela (cd) for light intensity, the mole (mol) for quantity of a substance, the radian (rad) for plane angles, and the steradian (sr) for solid angles.

## Derived units

Many physical phenomena are measured in units that are derived from SI units. As an example, frequency is measured in a unit known as the hertz (Hz). The hertz is the number of vibrations made by a wave in one second. It can be expressed in terms of the basic SI unit as s^{-1}. Pressure is another derived unit. Pressure is defined as the force per unit area. In the metric system, the unit of pressure is the Pascal (Pa) and can be expressed as kilograms per meter per second squared, or kg/m x^{2}. Even units that appear to have little or no relationship to the nine fundamental units can, nonetheless, be expressed in these terms. The absorbed dose, for example, indicates that amount of radiation received by a person or object. In the metric system, the unit for this measurement is the gray. One gray can be defined in terms of the fundamental units as meters squared per second squared, or m^{2} xs^{2}.

Many other commonly used units can also be expressed in terms of the nine fundamental units. Some of the most familiar are the units for area (square meter: m^{2}), volume (cubic meter: m^{3}), velocity (meters per second: m/s), concentration (moles per cubic meter: mol/m^{3}), density (kilogram per cubic meter: kg/m^{3}), luminance (candela per square meter: cd/m^{2}), and magnetic field strength (amperes per meter: A/m).

A set of prefixes is available that makes it possible to use the fundamental SI units to express larger or smaller amounts of the same quantity. Among the most commonly used prefixes are milli- (m) for one-thousandth, centi- (c) for one-hundredth, micro- (æ) for one-millionth, kilo- (k) for one thousand times, and mega- (M) for one million times. Thus, any volume can be expressed by using some combination of the fundamental unit (such as liter) and the appropriate prefix. One million liters, using this system, would be a megaliter (ML) and one millionth of a liter, a microliter (æL).

## Natural units

One characteristic of all of the above units is that they have been selected arbitrarily. The committee

### KEY TERMS

**British system** —A collection of measuring units that has developed haphazardly over many centuries and is now used almost exclusively in the United States and for certain specialized types of measurements.

**Derived units** —Units of measurements that can be obtained by multiplying or dividing various combinations of the nine basic SI units.

**Metric system** —A system of measurement developed in France in the 1790s.

**Natural units** —Units of measurement that are based on some obvious natural standard, such as the mass of an electron.

**SI system** —An abbreviation for Le Système International d’Unités, a system of weights and measures adopted in 1960 by the General Conference on Weights and Measures.

that established the metric system could, for example, have defined the meter as one one-hundredth the distance between Paris, France, and Sèvres, France. It was completely free to choose any standard it wished.

Some measurements, however, suggested natural units. In the field of electricity, for example, the charge carried by a single electron would appear to be a natural unit of measurement. That quantity is known as the elementary charge (e) and has the value of 1.6021892 × 10^{-19} coulomb. Other natural units of measurement include the speed of light (c: 2.99792458 × 10^{8} m/s), the Planck constant (6.626176 × 10^{-34} joule per hertz), the mass of an electron (m_{e}: 0.9109534 × 10^{-30} kg), and the mass of a proton (m_{p}: 1.6726485 × 10^{-27} kg). As one can see, each of these natural units can be expressed in terms of SI units, but they are often used as basic units in specialized fields of science.

## Unit conversions between systems

For many years, an effort has been made to have the metric system, including SI units, adopted worldwide. As early as 1866, the U.S. Congress legalized the use of the metric system. More than a hundred years later, in 1976, the Congress adopted the Metric Conversion Act, declaring it the policy of the nation to increase the use of the metric system in the United States.

In fact, little progress has been made in that direction. Indeed, elements of the British system of measurement continue in use for specialized purposes throughout the world. All flight navigation, for example, is expressed in terms of feet, not meters. As a consequence, it is still necessary for a person to be able to convert from one system of measurement to the other.

In 1959, English-speaking countries around the world met to adopt standard conversion factors between British and metric systems. To convert from the pound to the kilogram, for example, it is necessary to multiply the given quantity (in pounds) by the factor 0.45359237. A conversion in the reverse direction, from kilograms to pounds, involves multiplying the given quantity (in kilograms) by the factor 2.2046226. Other relevant conversion factors are 1 inch = 2.54 centimeters and 1 yard = 0.9144 meter.

## Resources

### BOOKS

Adams, Herbert F.R. *SI Metric Units: An Introduction*.Toronto: McGraw-Hill Ryerson, 1974.

Bureau International des Poids et Mesures. *Le Systeme International d’Unites (SI) [The International System of Units (SI)]*. Sevres, France: Bureau International des Poids et Mesures, 2006.

Burton, David M. *The History of Mathematics: An Introduction*. New York: McGraw-Hill, 2007.

Jerrard, H.G., and D.B. McNeil. *A Dictionary of Scientific Units: Including Dimensionless Numbers and Scales*. London, UK: Chapman and Hall, 1992.

Nelson, Robert A. SI: *The International System of Units*.Stony Brook, N.Y.: American Association of Physics Teachers, 1982.

Taylor, Barry N. (International Bureau of Weights and Measures). *The International System of Units (SI)*. Gaithersburg, MD: U.S. Department of Commerce, Technology Administration, National Institute of Standards and Technology, 2001.

David E. Newton