**Measurement** is the numerical quantitation of the attributes of an object or event, which can be used to compare with other objects or events.^{[1]}^{[2]} The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the *International vocabulary of metrology* published by the International Bureau of Weights and Measures.^{[2]} However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.^{[1]}^{[3]}

Measurement is a cornerstone of trade, science, technology, and quantitative research in many disciplines. Historically, many measurement systems existed for the varied fields of human existence to facilitate comparisons in these fields. Often these were achieved by local agreements between trading partners or collaborators. Since the 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern International System of Units (SI). This system reduces all physical measurements to a mathematical combination of seven base units. The science of measurement is pursued in the field of metrology.

In the field of survey research, measures are taken from individual attitudes, values, and behavior using questionnaires as a measurement instrument. As all other measurements, measurement in survey research is also vulnerable to measurement error, i.e. the departure from the true value of the measurement and the value provided using the measurement instrument.^{[14]} In substantive survey research, measurement error can lead to biased conclusions and wrongly estimated effects. In order to get accurate results, when measurement errors appear, the results need to be corrected for measurement errors.

The following rules generally apply for displaying the exactness of measurements:^{[15]}

- All non-0 digits and any 0s appearing between them are significant for the exactness of any number. For example, the number 12000 has two significant digits, and has implied limits of 11500 and 12500.
- Additional 0s may be added after a decimal separator to den
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 (about 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:

- This computation used for the acceleration of gravity 9.8 metres per second squared (32 ft/s
^{2}). But this measurement is not exact, but only precise to two significant digits. - The Earth's gravitational field varies slightly depending on height above sea level and other factors.
- The computation of 0.45 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.

Additionally, other sources of experimental error include:

- carelessness,
- determining of the exact time at which the object is released and the exact time it hits the ground,
- measurement of the height and the measurement of the time both involve some error,
- Air resistance.
- posture of human participants
^{[16]}

Scientific experiments 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.^{[17]}Quantity and measurement are mutually defined:Additionally, other sources of experimental error include:

- carelessness,
- determining of the exact time at which the object is released and the exact time it hits the ground,
- measurement of the height and the measurement of the time both involve some error,
- Air resistance.
- posture of human participants
^{[16]}

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

## Definitions and theories

Scientific experiments 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.^{[17]}Quantity and measurement are mutually defined: quantitative attributes are those 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.^{[17]}### Representational theory

In the representational theory,

*measurement*is defined as "the correlation of numbers with entities that are not numbers".^{[18]}The most technically elaborated form of representational theory is also known as [18] The most technically elaborated 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,^{[19]}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 measurem

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.

Three type of Representational theory

**1) Empirical relation**In science, an

**empirical relationship**is a**relationship**or correlation based solely on observation rather than theory. An**empirical relationship**requires only confirmatory data irrespective of theoretical basis**2) The rule of mapping**The real world is the Domain of mapping, and the mathematical world is the range. when we map the attribute to mathematical system, we have many choice for mapping and the range

**3) The representation condition of measurement**Information theory recognises 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."

^{[20]}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 expected 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 not a clear or neat distinction between estimation and measurement.### Quantum mechanics

In quantum mechanics, a measurement is an action that determines a particular property (position, momentum, energy, etc.) of a quantum system. Before a measurement is made, a quantum system is simultaneously described by all values in a range of possible values, where the probability of measuring each value is determined by the wavefunction of the system. When a measurement is performed, the wavefunction of the quantum system "collapses" to a single, definite value.

^{[21]}The unambiguous meaning of the measurement problem is an unresolved fundamental problem in quantum mechanics.^{[citation needed]}### Biology

In biology, there is no wel

In biology, there is no well established theory of measurement. However, the importance of the theoretical context is emphasized.

^{[22]}Moreover, the theoretical context stemming from the theory of evolution leads to articulate the theory of measurement and historicity as a fundamental notion.^{[23]}## See also

- This computation used for the acceleration of gravity 9.8 metres per second squared (32 ft/s