measurement

1. The act of measuring or the process of being measured.
2. A system of measuring: measurement in miles.
3. The dimension, quantity, or capacity determined by measuring: the measurements of a room.

From Metric to U.S. Customary Units

Temperature Conversion Between Celsius and Fahrenheit

U.S. Customary System: Length

U.S. Customary System: Volume or Capacity (Liquid Measure)

U.S. Customary System: Volume or Capacity (Dry Measure)

U.S. Customary System: Weight

U.S. Customary System: Geographic Area

Cooking Measures

British Imperial System: Volume or Capacity (Liquid Measure)

British Imperial System: Volume or Capacity (Dry Measure)

Apothecary Weights

Base Units

The International System has base units from which all others in the system are derived. The standards for the base units, except for the kilogram, are defined by unchanging and reproducible physical occurences. For example, the meter is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second. The standard for the kilogram is a platinum-iridium cylinder kept at the International Bureau of Weights and Standards in Sèvres, France.

Supplementary Units

The International System uses two supplementary units that are based on abstract geometrical concepts rather than physical standards.

Prefixes

A multiple of a unit in the International System is formed by adding a prefix to the name of that unit. The prefixes change the magnitude of the unit by orders of ten from 10 to 10.

Additional Units

Listed below are a few of the non-SI units that are commonly used with the International System.

Derived Units

Most of the units in the International System are derived units, that is units defined in terms of base units and supplementary units. Derived units can be divided into two groups - those that have a special name and symbol, and those that do not.

The process of determining values for numerical or categorical variables.

For more information on measurement, visit Britannica.com.

Concept

Measurement seems like a simple subject, on the surface at least; indeed, all measurements can be reduced to just two components: number and unit. Yet one might easily ask, "What numbers, and what units?"—a question that helps bring into focus the complexities involved in designating measurements. As it turns out, some forms of numbers are more useful for rendering values than others; hence the importance of significant figures and scientific notation in measurements. The same goes for units. First, one has to determine what is being measured: mass, length, or some other property (such as volume) that is ultimately derived from mass and length. Indeed, the process of learning how to measure reveals not only a fundamental component of chemistry, but an underlying—if arbitrary and manmade—order in the quantifiable world.

How It Works

Numbers

In modern life, people take for granted the existence of the base-10, of decimal numeration system—a name derived from the Latin word decem, meaning "ten." Yet there is nothing obvious about this system, which has its roots in the ten fingers used for basic counting. At other times in history, societies have adopted the two hands or arms of a person as their numerical frame of reference, and from this developed a base-2 system. There have also been base-5 systems relating to the fingers on one hand, and base-20 systems that took as their reference point the combined number of fingers and toes.

Obviously, there is an arbitrary quality underlying the modern numerical system, yet it works extremely well. In particular, the use of decimal fractions (for example, 0.01 or 0.235) is particularly helpful for rendering figures other than whole numbers. Yet decimal fractions are a relatively recent innovation in Western mathematics, dating only to the sixteenth century. In order to be workable, decimal fractions rely on an even more fundamental concept that was not always part of Western mathematics: place-value.

Place-Value and Notation Systems

Place-value is the location of a number relative to others in a sequence, a location that makes it possible to determine the number's value. For instance, in the number 347, the 3 is in the hundreds place, which immediately establishes a value for the number in units of 100. Similarly, a person can tell at a glance that there are 4 units of 10, and 7 units of 1.

Of course, today this information appears to be self-evident—so much so that an explanation of it seems tedious and perfunctory—to almost anyone who has completed elementary-school arithmetic. In fact, however, as with almost everything about numbers and units, there is nothing obvious at all about place-value; otherwise, it would not have taken Western mathematicians thousands of years to adopt a place-value numerical system. And though they did eventually make use of such a system, Westerners did not develop it themselves, as we shall see.

Roman Numerals

Numeration systems of various kinds have existed since at least 3000 B.C., but the most important number system in the history of Western civilization prior to the late Middle Ages was the one used by the Romans. Rome ruled much of the known world in the period from about 200 B.C. to about A.D. 200, and continued to have an influence on Europe long after the fall of the Western Roman Empire in A.D. 476—an influence felt even today. Though the Roman Empire is long gone and Latin a dead language, the impact of Rome continues: thus, for instance, Latin terms are used to designate species in biology. It is therefore easy to understand how Europeans continued to use the Roman numeral system up until the thirteenth century A.D.—despite the fact that Roman numerals were enormously cumbersome.

The Roman notation system has no means of representing place-value: thus a relatively large number such as 3,000 is shown as MMM, whereas a much smaller number might use many more "places": 438, for instance, is rendered as CDXXXVIII. Performing any sort of calculations with these numbers is a nightmare. Imagine, for instance, trying to multiply these two. With the number system in use today, it is not difficult to multiply 3,000 by 438 in one's head. The problem can be reduced to a few simple steps: multiply 3 by 400, 3 by 30, and 3 by 8; add these products together; then multiply the total by 1,000—a step that requires the placement of three zeroes at the end of the number obtained in the earlier steps.

But try doing this with Roman numerals: it is essentially impossible to perform this calculation without resorting to the much more practical place-value system to which we're accustomed. No wonder, then, that Roman numerals have been relegated to the sidelines, used in modern life for very specific purposes: in outlines, for instance; in ordinal titles (for example, Henry VIII); or in designating the year of a motion picture's release.

Hindu-Arabic Numerals

The system of counting used throughout much of the world—1, 2, 3, and so on—is the Hindu-Arabic notation system. Sometimes mistakenly referred to as "Arabic numerals," these are most accurately designated as Hindu or Indian numerals. They came from India, but because Europeans discovered them in the Near East during the Crusades (1095-1291), they assumed the Arabs had invented the notation system, and hence began referring to them as Arabic numerals.

Developed in India during the first millennium B.C., Hindu notation represented a vast improvement over any method in use up to or indeed since that time. Of particular importance was a number invented by Indian mathematicians: zero. Until then, no one had considered zero worth representing since it was, after all, nothing. But clearly the zeroes in a number such as 2,000,002 stand for something. They perform a place-holding function: otherwise, it would be impossible to differentiate between 2,000,002 and 22.

Uses of Numbers in Science

Scientific Notation

Chemists and other scientists often deal in very large or very small numbers, and if they had to write out these numbers every time they discussed them, their work would soon be encumbered by lengthy numerical expressions. For this purpose, they use scientific notation, a method for writing extremely large or small numbers by representing them as a number between 1 and 10 multiplied by a power of 10.

Instead of writing 75,120,000, for instance, the preferred scientific notation is 7.512 · 10⁷. To interpret the value of large multiples of 10, it is helpful to remember that the value of 10 raised to any power n is the same as 1 followed by that number of zeroes. Hence 10²⁵, for instance, is simply 1 followed by 25 zeroes.

Scientific notation is just as useful—to chemists in particular—for rendering very small numbers. Suppose a sample of a chemical compound weighed 0.0007713 grams. The preferred scientific notation, then, is 7.713 · 10⁻⁴. Note that for numbers less than 1, the power of 10 is a negative number: 10⁻¹ is 0.1, 10⁻² is 0.01, and so on.

Again, there is an easy rule of thumb for quickly assessing the number of decimal places where scientific notation is used for numbers less than 1. Where 10 is raised to any power −n, the decimal point is followed by n places. If 10 is raised to the power of −8, for instance, we know at a glance that the decimal is followed by 7 zeroes and a 1.

Significant Figures

In making measurements, there will always be a degree of uncertainty. Of course, when the standards of calibration (discussed below) are very high, and the measuring instrument has been properly calibrated, the degree of uncertainty will be very small. Yet there is bound to be uncertainty to some degree, and for this reason, scientists use significant figures—numbers included in a measurement, using all certain numbers along with the first uncertain number.

Suppose the mass of a chemical sample is measured on a scale known to be accurate to 10⁻⁵, kg. This is equal to 1/100,000 of a kilo, or 1/100 of a gram; or, to put it in terms of place-value, the scale is accurate to the fifth place in a decimal fraction. Suppose, then, that an item is placed on the scale, and a reading of 2.13283697 kg is obtained. All the numbers prior to the 6 are significant figures, because they have been obtained with certainty. On the other hand, the 6 and the numbers that follow are not significant figures because the scale is not known to be accurate beyond 10⁻⁵ kg.

Thus the measure above should be rendered with 7 significant figures: the whole number 2, and the first 6 decimal places. But if the value is given as 2.132836, this might lead to inaccuracies at some point when the measurement is factored into other equations. The 6, in fact, should be "rounded off" to a 7. Simple rules apply to the rounding off of significant figures: if the digit following the first uncertain number is less than 5, there is no need to round off. Thus, if the measurement had been 2.13283627 kg (note that the 9 was changed to a 2), there is no need to round off, and in this case, the figure of 2.132836 is correct. But since the number following the 6 is in fact a 9, the correct significant figure is 7; thus the total would be 2.132837.

Fundamental Standards of Measure

So much for numbers; now to the subject of units. But before addressing systems of measurement, what are the properties being measured? All forms of scientific measurement, in fact, can be reduced to expressions of four fundamental properties: length, mass, time, and electric current. Everything can be expressed in terms of these properties: even the speed of an electron spinning around the nucleus of an atom can be shown as "length" (though in this case, the measurement of space is in the form of a circle or even more complex shapes) divided by time.

Of particular interest to the chemist are length and mass: length is a component of volume, and both length and mass are elements of density. For this reason, a separate essay in this book is devoted to the subject of Mass, Density, and Volume. Note that "length," as used in this most basic sense, can refer to distance along any plane, or in any of the three dimensions—commonly known as length, width, and height—of the observable world. (Time is the fourth dimension.) In addition, as noted above, "length" measurements can be circular, in which case the formula for measuring space requires use of the coefficient π, roughly equal to 3.14.

Real-Life Applications

Standardized Units of Measure: Who Needs Them?

People use units of measure so frequently in daily life that they hardly think about what they are doing. A motorist goes to the gas station and pumps 13 gallons (a measure of volume) into an automobile. To pay for the gas, the motorist uses dollars—another unit of measure, economic rather than scientific—in the form of paper money, a debit card, or a credit card.

This is simple enough. But what if the motorist did not know how much gas was in a gallon, or if the motorist had some idea of a gallon that differed from what the gas station management determined it to be? And what if the value of a dollar were not established, such that the motorist and the gas station attendant had to haggle over the cost of the gasoline just purchased? The result would be a horribly confused situation: the motorist might run out of gas, or money, or both, and if such confusion were multiplied by millions of motorists and millions of gas stations, society would be on the verge of breakdown.

The Value of Standardization to a Society

Actually, there have been times when the value of currency was highly unstable, and the result was near anarchy. In Germany during the early 1920s, for instance, rampant inflation had so badly depleted the value of the mark, Germany's currency, that employees demanded to be paid every day so that they could cash their paychecks before the value went down even further. People made jokes about the situation: it was said, for instance, that when a woman went into a store and left a basket containing several million marks out front, thieves ran by and stole the basket—but left the money. Yet there was nothing funny about this situation, and it paved the way for the nightmarish dictatorship of Adolf Hitler and the Nazi Party.

It is understandable, then, that standardization of weights and measures has always been an important function of government. When Ch'in Shih-huang-ti (259-210 B.C.) united China for the first time, becoming its first emperor, he set about standardizing units of measure as a means of providing greater unity to the country—thus making it easier to rule. On the other hand, the Russian Empire of the late nineteenth century failed to adopt standardized systems that would have tied it more closely to the industrialized nations of Western Europe. The width of railroad tracks in Russia was different than in Western Europe, and Russia used the old Julian calendar, as opposed to the Gregorian calendar adopted throughout much of Western Europe after 1582. These and other factors made economic exchanges between Russia and Western Europe extremely difficult, and the Russian Empire remained cut off from the rapid progress of the West. Like Germany a few decades later, it became ripe for the establishment of a dictatorship—in this case under the Communists led by V. I. Lenin.

Aware of the important role that standardization of weights and measures plays in the governing of a society, the U.S. Congress in 1901 established the Bureau of Standards. Today it is known as the National Institute of Standards and Technology (NIST), a nonregulatory agency within the Commerce Department. As will be discussed at the conclusion of this essay, the NIST maintains a wide variety of standard definitions regarding mass, length, temperature and so forth, against which other devices can be calibrated.

The Value of Standardization to Science

What if a nurse, rather than carefully measuring a quantity of medicine before administering it to a patient, simply gave the patient an amount that "looked right"? Or what if a pilot, instead of calculating fuel, distance, and other factors carefully before taking off from the runway, merely used a "best estimate"? Obviously, in either case, disastrous results would be likely to follow. Though neither nurses or pilots are considered scientists, both use science in their professions, and those disastrous results serve to highlight the crucial matter of using standardized measurements in science.

Standardized measurements are necessary to a chemist or any scientist because, in order for an experiment to be useful, it must be possible to duplicate the experiment. If the chemist does not know exactly how much of a certain element he or she mixed with another to form a given compound, the results of the experiment are useless. In order to share information and communicate the results of experiments, then, scientists need a standardized "vocabulary" of measures.

This "vocabulary" is the International System of Units, known as SI for its French name, Système International d'Unités. By international agreement, the worldwide scientific community adopted what came to be known as SI at the 9th General Conference on Weights and Measures in 1948. The system was refined at the 11th General Conference in 1960, and given its present name; but in fact most components of SI belong to a much older system of weights and measures developed in France during the late eighteenth century.

Si Vs. the English System

The United States, as almost everyone knows, is the wealthiest and most powerful nation on Earth. On the other hand, Brunei—a tiny nation-state on the island of Java in the Indonesian archipelago—enjoys considerable oil wealth, but is hardly what anyone would describe as a super-power. Yemen, though it is located on the Arabian peninsula, does not even possess significant oil wealth, and is a poor, economically developing nation. Finally, Burma in Southeast Asia can hardly be described even as a "developing" nation: ruled by an extremely repressive military regime, it is one of the poorest nations in the world.

So what do these four have in common? They are the only nations on the planet that have failed to adopt the metric system of weights and measures. The system used in the United States is called the English system, though it should more properly be called the American system, since England itself has joined the rest of the world in "going metric." Meanwhile, Americans continue to think in terms of gallons, miles, and pounds; yet American scientists use the much more convenient metric units that are part of SI.

How the English System Works (or Does Not Work)

Like methods of counting described above, most systems of measurement in premodern times were modeled on parts of the human body. The foot is an obvious example of this, while the inch originated from the measure of a king's first thumb joint. At one point, the yard was defined as the distance from the nose of England's King Henry I to the tip of his outstretched middle finger.

Obviously, these are capricious, downright absurd standards on which to base a system of measure. They involve things that change, depending for instance on whose foot is being used as a standard. Yet the English system developed in this willy-nilly fashion over the centuries; today, there are literally hundreds of units—including three types of miles, four kinds of ounces, and five kinds of tons, each with a different value.

What makes the English system particularly cumbersome, however, is its lack of convenient conversion factors. For length, there are 12 inches in a foot, but 3 feet in a yard, and 1,760 yards in a mile. Where volume is concerned, there are 16 ounces in a pound (assuming one is talking about an avoirdupois ounce), but 2,000 pounds in a ton. And, to further complicate matters, there are all sorts of other units of measure developed to address a particular property: horsepower, for instance, or the British thermal unit (Btu).

The Convenience of the Metric System

Great Britain, though it has long since adopted the metric system, in 1824 established the British Imperial System, aspects of which are reflected in the system still used in America. This is ironic, given the desire of early Americans to distance themselves psychologically from the empire to which their nation had once belonged. In any case, England's great worldwide influence during the nineteenth century brought about widespread adoption of the English or British system in colonies such as Australia and Canada. This acceptance had everything to do with British power and tradition, and nothing to do with convenience. A much more usable standard had actually been embraced 25 years before in a land that was then among England's greatest enemies: France.

During the period leading up to and following the French Revolution of 1789, French intellectuals believed that every aspect of existence could and should be treated in highly rational, scientific terms. Out of these ideas arose much folly, particularly during the Reign of Terror in 1793, but one of the more positive outcomes was the metric system. This system is decimal—that is, based entirely on the number 10 and powers of 10, making it easy to relate one figure to another. For instance, there are 100 centimeters in a meter and 1,000 meters in a kilometer.

Prefixes for Sizes in the Metric System

For designating smaller values of a given measure, the metric system uses principles much simpler than those of the English system, with its irregular divisions of (for instance) gallons, quarts, pints, and cups. In the metric system, one need only use a simple Greek or Latin prefix to designate that the value is multiplied by a given power of 10. In general, the prefixes for values greater than 1 are Greek, while Latin is used for those less than 1. These prefixes, along with their abbreviations and respective values, are as follows. (The symbol μ for "micro" is the Greek letter mu.)

The Most Commonly Used Prefixes in the Metric System

• giga (G) = 10⁹ (1,000,000,000)
• mega (M) = 10⁶ (1,000,000)
• kilo (k) == 10³ (1,000)
• deci (d) = 10⁻¹ (0.1)
• centi (c) = 10⁻² (0.01)
• milli (m) = 10⁻³ (0.001)
• micro (μ) = 10⁻⁶ (0.000001)
• nano (n) = 10⁻⁹ (0.000000001)

The use of these prefixes can be illustrated by reference to the basic metric unit of length, the meter. For long distances, a kilometer (1,000 m) is used; on the other hand, very short distances may require a centimeter (0.01 m) or a millimeter (0.001 m) and so on, down to a nanometer (0.000000001 m). Measurements of length also provide a good example of why SI includes units that are not part of the metric system, though they are convertible to metric units. Hard as it may be to believe, scientists often measure lengths even smaller than a nanometer—the width of an atom, for instance, or the wavelength of a light ray. For this purpose, they use the angstrom (Å or A), equal to 0.1 nanometers.

Calibration and Si Units

The Seven Basic Si Units

The SI uses seven basic units, representing length, mass, time, temperature, amount of substance, electric current, and luminous intensity. The first four parameters are a part of everyday life, whereas the last three are of importance only to scientists. "Amount of substance" is the number of elementary particles in matter. This is measured by the mole, a unit discussed in the essay on Mass, Density, and Volume. Luminous intensity, or the brightness of a light source, is measured in candelas, while the SI unit of electric current is the ampere.

The other four basic units are the meter for length, the kilogram for mass, the second for time, and the degree Celsius for temperature. The last of these is discussed in the essay on Temperature; as for meters, kilograms, and seconds, they will be examined below in terms of the means used to define each.

Calibration

Calibration is the process of checking and correcting the performance of a measuring instrument or device against the accepted standard. America's preeminent standard for the exact time of day, for instance, is the United States Naval Observatory in Washington, D.C. Thanks to the Internet, people all over the country can easily check the exact time, and calibrate their clocks accordingly—though, of course, the resulting accuracy is subject to factors such as the speed of the Internet connection.

There are independent scientific laboratories responsible for the calibration of certain instruments ranging from clocks to torque wrenches, and from thermometers to laser-beam power analyzers. In the United States, instruments or devices with high-precision applications—that is, those used in scientific studies, or by high-tech industries—are calibrated according to standards established by the NIST.

The NIST keeps on hand definitions, as opposed to using a meter stick or other physical model. This is in accordance with the methods of calibration accepted today by scientists: rather than use a standard that might vary—for instance, the meter stick could be bent imperceptibly—unvarying standards, based on specific behaviors in nature, are used.

Meters and Kilograms

A meter, equal to 3.281 feet, was at one time defined in terms of Earth's size. Using an imaginary line drawn from the Equator to the North Pole through Paris, this distance was divided into 10 million meters. Later, however, scientists came to the realization that Earth is subject to geological changes, and hence any measurement calibrated to the planet's size could not ultimately be reliable. Today the length of a meter is calibrated according to the amount of time it takes light to travel through that distance in a vacuum (an area of space devoid of air or other matter). The official definition of a meter, then, is the distance traveled by light in the interval of 1/299,792,458 of a second.

One kilogram is, on Earth at least, equal to 2.21 pounds; but whereas the kilogram is a unit of mass, the pound is a unit of weight, so the correspondence between the units varies depending on the gravitational field in which a pound is measured. Yet the kilogram, though it represents a much more fundamental property of the physical world than a pound, is still a somewhat arbitrary form of measure in comparison to the meter as it is defined today.

Given the desire for an unvarying standard against which to calibrate measurements, it would be helpful to find some usable but unchanging standard of mass; unfortunately, scientists have yet to locate such a standard. Therefore, the value of a kilogram is calibrated much as it was two centuries ago. The standard is a bar of platinum-iridium alloy, known as the International Prototype Kilogram, housed near Sévres in France.

Seconds

A second, of course, is a unit of time as familiar to non-scientifically trained Americans as it is to scientists and people schooled in the metric system. In fact, it has nothing to do with either the metric system or SI. The means of measuring time on Earth are not "metric": Earth revolves around the Sun approximately every 365.25 days, and there is no way to turn this into a multiple of 10 without creating a situation even more cumbersome than the English units of measure.

The week and the month are units based on cycles of the Moon, though they are no longer related to lunar cycles because a lunar year would soon become out-of-phase with a year based on Earth's rotation around the Sun. The continuing use of weeks and months as units of time is based on tradition—as well as the essential need of a society to divide up a year in some way.

A day, of course, is based on Earth's rotation, but the units into which the day is divided—hours, minutes, and seconds—are purely arbitrary, and likewise based on traditions of long standing. Yet scientists must have some unit of time to use as a standard, and, for this purpose, the second was chosen as the most practical. The SI definition of a second, however, is not simply one-sixtieth of a minute or anything else so strongly influenced by the variation of Earth's movement.

Instead, the scientific community chose as its standard the atomic vibration of a particular isotope of the metal cesium, cesium-133. The vibration of this atom is presumed to be unvarying, because the properties of elements—unlike the size of Earth or its movement—do not change. Today, a second is defined as the amount of time it takes for a cesium-133 atom to vibrate 9,192,631,770 times. Expressed in scientific notation, with significant figures, this is 9.19263177 · 10⁹.

Where to Learn More

Gardner, Robert. Science Projects About Methods of Measuring. Berkeley Heights, N.J.: Enslow Publishers, 2000.

Long, Lynette. Measurement Mania: Games and ActivitiesThat Make Math Easy and Fun. New York: Wiley, 2001.

"Measurement" (Web site). <http://www.dist214.k12.il.us/users/asanders/meas.html> (May 7, 2001).

"Measurement in Chemistry" (Web site). <http://bradley.edu/~campbell/lectnotes/149ch2/tsld001.htm> (May7, 2001).

MegaConverter 2 (Web site). <http://www.megaconverter.com> (May 7, 2001).

Patilla, Peter. Measuring. Des Plaines, IL: Heinemann Library, 2000.

Richards, Jon. Units and Measurements. Brookfield, CT: Copper Beech Books, 2000.

Sammis, Fran. Measurements. New York: Benchmark Books, 1998.

Units of Measurement (Web site). <http://www.unc.edu/~rowlett/units/> (May 7, 2001).

Wilton High School Chemistry Coach (Web site). <http://www.chemistrycoach.com> (May 7, 2001).

noun

The act or process of ascertaining dimensions, quantity, or capacity: measure, mensuration, metrology. See big/small/amount.

Definition: calculation
Antonyms: estimate, guess

The fundamental concepts of the theory of measurement are that of a quantity being measured, an empirical determination for a lesser, equal, or greater amount of the quantity, and then a rule assigning numerical values to the quantities empirically determined. Different quantities are therefore represented by different numbers. The rule must require procedures for assigning the same numerals to the same things under the same conditions, and it must be nondegenerate, in the sense that the rule allows for the possibility of assigning different numerals to different things, or the same thing under different conditions. The rule then defines a scale from the least value of the quantity to the greatest. Moh's hardness scale is an ordering of minerals from the softest (talc, 1) to the hardest (diamond, 10). Such a scale gives no sense to the idea of one point on the scale (say, orthoclase, 6) being twice as hard as another (calcite, 3), nor to the question of whether the difference between one pair of intervals on the scale is the same as that of another. In the terminology of Brian Ellis, Basic Concepts of Measurement (1966), Moh's scale is simply an ordering, or an ordinal scale. Features that can be ordered but no more, are sometimes called qualitative, or non-metric. If, in addition, formulae providing for the absolute sameness or difference of intervals on the scale can be interpreted, we have an interval scale; if such intervals can be compared we have an ordinal-interval scale; and if a = nb can be interpreted where (a,b) are numbers on the scale and n is any positive integer, we have a ratio scale. The date scales of the calendar are ordinal-interval scales, whereas ordinary scales of mass, length, and time are ratio scales. Questions for the philosophy of science include the nature and objectivity of measurement, the question of whether the same quantity can be measured by scales which are not simple transformations of one another (as the Celsius and Fahrenheit scales of temperature are), and the nature of the considerations, such as mathematical simplicity, that guide the choice of fundamental scales for measuring physical quantities. In particular disciplines, for instance economics, the question of whether a quantity such as utility or welfare is purely qualitative, or is susceptible of more structured measurement, may assume great importance. Similarly philosophical, scientific, and pragmatic considerations affect finding the correct quantities to measure in order to understand multi-dimensional complexes such as an economy or a society.

Ascertaining a dimension by the physical act of measurement.

• discretizing m. — see discretizing measurements.

If we dream about something being measured out, it may represent a feeling of waiting, of "How long will this last?" It could also allude to the fact that we are making comparisons in our waking life.

"Measurements" redirects here. For the disused railway station in Oldham, see Measurements railway station.

For bust/waist/hip measurement, see BWH.

In science, measurement is the process of obtaining the magnitude of a quantity, such as length or mass, relative to a unit of measurement, such as a meter or a kilogram. The term can also be used to refer to the result obtained after performing the process.

Contents 1 History 2 Standards 3 Units and systems 3.1 Imperial system 3.2 Metric system 3.3 SI 3.3.1 Converting prefixes 3.4 Distance 4 Some special names 4.1 Building trades 4.2 Time 4.3 Mass 4.4 Economics 5 Difficulties 6 Definitions and theories 6.1 Classical definition 6.2 Representational theory 6.3 Information theory 6.4 Quantum mechanics 7 In physics 8 See also 9 References 10 External links

History

Main article: History of measurement

The word "measurement" is derived from the Greek word "metron" which means a limited proportion.

The history of measurements is a topic within the history of science and technology.

Standards

Laws to regulate measurement were originally developed to prevent fraud. However, units of measurement are now generally defined on a scientific basis, and are established by international treaties. In the United States, the National Institute of Standards and Technology (NIST), a division of the United States Department of Commerce, regulates commercial measurements. In the United Kingdom, the role is performed by the National Physical Laboratory (NPL).

Units and systems

Main articles: Units of measurement and Systems of measurement

A baby bottle that measures in all three measurement systems, Imperial (U.K.), U.S. Customary, and metric.

The definition or specification of precise standards of measurement involves two key features, which are evident in the International System of Units (SI). Specifically, in this system the definition of each of the base units refer to specific empirical conditions and, with the exception of the kilogram, also to other quantitative attributes. Each derived SI unit is defined purely in terms of a relationship involving it and other units; for example, the unit of velocity is 1 m/s. Because derived units refer to base units, the specification of empirical conditions is an implied component of the definition of all units.

Imperial system

Main article: Imperial Unit

Before SI units were widely adopted around the world, the British systems of English units and later Imperial units were used in Britain, the Commonwealth and the United States. The system came to be known as U.S. customary units in the United States and is still in use there and in a few Caribbean countries. These various systems of measurement have at times been called foot-pound-second systems after the Imperial units for distance, weight and time even though the tons, hundredweights, gallons, and nautical miles, for example, are different for the U.S. units. Many Imperial units remain in use in Britain despite the fact that it has officially switched to the SI system. Road signs are still in miles, yards, miles per hour, and so on, people tend to measure their own height in feet and inches and milk is sold in pints, to give just a few examples. Imperial units are used in many other places, for example, in many Commonwealth countries that are considered metricated, land area is measured in acres and floor space in square feet, particularly for commercial transactions (rather than government statistics). Similarly, the imperial gallon is used in many countries that are considered metricated at gas/petrol stations, an example b

Metric system

Main article: Metric system

The metric system is a decimalized system of measurement based on the metre and the gram. It exists in several variations, with different choices of base units, though these do not affect its day-to-day use. Since the 1960s, the International System of Units (SI), explained further below, is the internationally recognized standard metric system. Metric units of mass, length, and electricity are widely used around the world for both everyday and scientific purposes. The main advantage of the metric system is that it has a single base unit for each physical quantity. All other units are powers of ten or multiples of ten of this base unit. Unit conversions are always simple because they will be in the ratio of ten, one hundred, one thousand, etc. All lengths and distances, for example, are measured in meters, or thousandths of a metre (millimeters), or thousands of meters (kilometres), and so on. There is no profusion of different units with different conversion factors as in the Imperial system (e.g. inches, feet, yards, fathoms, rods). Multiples and submultiples are related to the fundamental unit by factors of powers of ten, so that one can convert by simply moving the decimal place: 1.234 metres is 1234 millimetres or 0.001234 kilometres. The use of fractions, such as 2/5 of a meter, is not prohibited, but uncommon.

SI

Main article: International System of Units

The International System of Units (abbreviated SI from the French language name Système International d'Unités) is the modern, revised form of the metric system. It is the world's most widely used system of units, both in everyday commerce and in science. The SI was developed in 1960 from the metre-kilogram-second (MKS) system, rather than the centimetre-gram-second (CGS) system, which, in turn, had many variants. At its development the SI also introduced several newly named units that were previously not a part of the metric system. The SI units for the four basic physical quantities: length, time, mass, and temperature are:

1. meter (m)  :SI unit of length
2. second (s)  :SI unit of time
3. kilogram (kg) :SI unit of mass
4. kelvin (K)  :SI unit of temperature

There are two types of SI units, base and derived units. Base units are the simple measurements for time, length, mass, temperature, amount of substance, electric current and light intensity. Derived units are made up of base units, for example, density is kg/m³.

Converting prefixes

The SI allows easy multiplication when switching among units having the same base but different prefixes. To convert from metres to centimetres it is only necessary to multiply the number of metres by 100, since there are 100 centimetres in a metre. Inversely, to switch from centimetres to metres one multiplies the number of centimetres by 0.01 or divide centimetres by 100.

Distance

A 2-metre carpenter's ruler

A ruler or rule is a tool used in, for example, geometry, technical drawing, engineering, and carpentry, to measure distances or to draw straight lines. Strictly speaking, the ruler is the instrument used to rule straight lines and the calibrated instrument used for determining length is called a measure, however common usage calls both instruments rulers and the special name straightedge is used for an unmarked rule. The use of the word measure, in the sense of a measuring instrument, only survives in the phrase tape measure, an instrument that can be used to measure but cannot be used to draw straight lines. As can be seen in the photographs on this page, a two-metre carpenter's rule can be folded down to a length of only 20 centimetres, to easily fit in a pocket, and a five-metre long tape measure easily retracts to fit within a small housing.

Some special names

We also use some special names for some multiples of some units.

• 100 kilograms = 1 quintal;1000 kilogram = 1 metric tonne;
• 10 years = 1 decade; 100 years = 1 century; 1000 years = 1 millennium

Building trades

The Australian building trades adopted the metric system in 1966 and the units used for measurement of length are metres (m) and millimetres (mm). Centimetres (cm) are avoided as they cause confusion when reading plans, the length two and a half metres is usually recorded as 2500 mm or 2.5 m.

Time

Main article: Time

Mass

Main article: Weighing scale

Mass refers to the intrinsic property of all material objects to resist changes in their momentum. Weight, on the other hand, refers to the downward force produced when a mass is in a gravitational field. In free fall, objects lack weight but retain their mass. The Imperial units of mass include the ounce, pound, and ton. The metric units gram and kilogram are units of mass.

A unit for measuring weight or mass is called a weighing scale or, often, simply a scale. A spring scale measures force but not mass, a balance compares masses, but requires a gravitational field to operate. The most accurate instrument for measuring weight or mass is the digital scale, but it also requires a gravitational field, and would not work in free fall.

Economics

Main article: Measurement in economics

The measures used in economics are physical measures, nominal price value measures and fixed price value measures. These measures differ from one another by the variables they measure and by the variables excluded from measurements. The measurable variables in economics are quantity, quality and distribution. By excluding variables from measurement makes it possible to better focus the measurement on a given variable, yet, this means a narrower approach.

Difficulties

Since accurate measurement is essential in many fields, and since all measurements are necessarily approximations, a great deal of effort must be taken to make measurements as accurate as possible. For example, consider the problem of measuring the time it takes an object to fall a distance of one metre (39 in). Using physics, it can be shown that, in the gravitational field of the Earth, it should take any object about 0.45 second to fall one metre. However, the following are just some of the sources of error that arise. First, this computation used for the acceleration of gravity 9.8 metres per second per second (32.2 ft/s²). But this measurement is not exact, but only precise to two significant digits. Also, the Earth's gravitational field varies slightly depending on height above sea level and other factors. Next, the computation of .45 seconds involved extracting a square root, a mathematical operation that required rounding off to some number of significant digits, in this case two significant digits.

So far, we have only considered scientific sources of error. In actual practice, dropping an object from a height of a metre stick and using a stopwatch to time its fall, we have other sources of error. First, and most common, is simple carelessness. Then there is the problem of determining the exact time at which the object is released and the exact time it hits the ground. There is also the problem that the measurement of the height and the measurement of the time both involve some error. Finally, there is the problem of air resistance.

Scientific measurements must be carried out with great care to eliminate as much error as possible, and to keep error estimates realistic.

Definitions and theories

Classical definition

In the classical definition, which is standard throughout the physical sciences, measurement is the determination or estimation of ratios of quantities. Quantity and measurement are mutually defined: quantitative attributes are those, which it is possible to measure, at least in principle. The classical concept of quantity can be traced back to John Wallis and Isaac Newton, and was foreshadowed in Euclid's Elements.^{[citation needed]}

Representational theory

In the representational theory, measurement is defined as "the correlation of numbers with entities that are not numbers"^[1]. The strongest form of representational theory is also known as additive conjoint measurement. In this form of representational theory, numbers are assigned based on correspondences or similarities between the structure of number systems and the structure of qualitative systems. A property is quantitative if such structural similarities can be established. In weaker forms of representational theory, such as that implicit within the work of Stanley Smith Stevens^[2], numbers need only be assigned according to a rule.

The concept of measurement is often misunderstood as merely the assignment of a value, but it is possible to assign a value in a way that is not a measurement in terms of the requirements of additive conjoint measurement. One may assign a value to a person's height, but unless it can be established that there is a correlation between measurements of height and empirical relations, it is not a measurement according to additive conjoint measurement theory. Likewise, computing and assigning arbitrary values, like the "book value" of an asset in accounting, is not a measurement because it does not satisfy the necessary criteria.

Information theory

Information theory recognizes that all data are inexact and statistical in nature. Thus the definition of measurement is: "A set of observations that reduce uncertainty where the result is expressed as a quantity."^[3]. This definition is implied in what scientists actually do when they measure something and report both the mean and statistics of the measurements. In practical terms, one begins with an initial guess as to the value of a quantity, and then, using various methods and instruments, reduces the uncertainty in the value. Note that in this view, unlike the positivist representational theory, all measurements are uncertain, so instead of assigning one value, a range of values is assigned to a measurement. This also implies that there is a continuum between estimation and measurement.

Quantum mechanics

In quantum mechanics, a measurement is the "collapse of the wavefunction". The unambiguous meaning of the measurement problem is an unresolved fundamental problem in quantum mechanics.

In physics

Measuring the ratios between physical quantities is an important sub-field of physics.

Some important physical quantities include:

• Elementary charge (electric charge of electrons, protons, etc.)
• Fine-structure constant
• Gravitational constant
• Planck's constant
• Quantity
• Speed of light

See also

Airy points Conversion of units Detection limit Differential linearity Dimensional analysis Dimensionless number Econometrics History of measurement Instrumentation Key relevance in locksmithing Levels of measurement Measurement in quantum mechanics Measuring instrument NCSL International

Number sense Orders of magnitude Psychometrics Statistics Systems of measurement Test method Timeline of temperature and pressure measurement technology Timeline of time measurement technology Units of measurement Uncertainty principle Uncertainty in measurement Virtual instrumentation Weights and measures

References

1. ^ Ernest Nagel: "Measurement", Erkenntnis, Volume 2, Number 1 / December, 1931, pp. 313-335, published by Springer, the Netherlands
2. ^ Stevens, S.S. On the theory of scales and measurement 1946. Science. 103, 677-680.
3. ^ Douglas Hubbard: "How to Measure Anything", Wiley (2007), p. 21

External links

Look up measurement in Wiktionary, the free dictionary.

• BIPM International Vocabulary of Measurement (VIM)
• 'Universcale', an application showing the relative sizes of objects
• A Dictionary of Units of Measurement
• Comprehensive Unit Conversion Calculator
• 'Metrology – in short' 3rd edition, July 2008 ISBN 978-87-988154-5-7
• Measurement and Metrology Terms - English/German Dictionary
• Common measurement conversions
• Naming measuring implements

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Dansk (Danish)
n. - (op)måling, mål

Nederlands (Dutch)
maat, afmeting, meting

Français (French)
n. - dimensions, (Cout) mensurations, tour (de taille), longueur (de jambe)

Deutsch (German)
n. - Messung, Maße

Ελληνική (Greek)
n. - μέτρηση, (πληθ.) διαστάσεις, μέτρα

Italiano (Italian)
misura

Português (Portuguese)
n. - medição (f)

Русский (Russian)
измерение, размеры, система мер

Español (Spanish)
n. - medición, medida, dimensiones

Svenska (Swedish)
n. - mätning

中文（简体）(Chinese (Simplified))
测量法, 尺寸, 度量

中文（繁體）(Chinese (Traditional))
n. - 測量法, 尺寸, 度量

한국어 (Korean)
n. - 치수, 측정

日本語 (Japanese)
n. - 測量, 度量法, 測定値, 寸法, 大きさ, サイズ

العربيه (Arabic)
‏(الاسم) قياسات‏

עברית (Hebrew)
n. - ‮מדידה, מידה‬

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