determination of the magnitude of a quantity by comparison with a standard for that quantity. Quantities frequently measured include time, length, area, volume, pressure, mass, force, and energy. To express a measurement, there must be a basic unit of the quantity involved, e.g., the inch or second, and a standard of measurement (instrument) calibrated in such units, e.g., a ruler or clock. For convenience, such a standard is usually marked off both in multiples and in fractions of the basic unit. Although various systems of units exist for measuring different quantities (see weights and measures), the most important and widely used are the metric system and the English units of measurement. Certain units have been defined for special applications, e.g., the light-year and parsec in astronomy and the angstrom in physics. Measurement is one of the fundamental processes of science. It provides the data on which new theories are based and by which older theories are tested and retested. A good measurement should be both accurate and precise. Accuracy is determined by the care taken by the person making the measurement and the condition of the instrument; a worn or broken instrument or one carelessly used may give an inaccurate result. Precision, on the other hand, is determined by the design of the instrument; the finer the graduations on the instrument's scale and the greater the ease with which they can be read, the more precise the measurement. The choice of the instrument used should be appropriate to the desired precision of the results. The human foot may be a suitable instrument for pacing off short distances if precision is not important; at the other extreme, the interferometer (see interference) is used for extremely precise measurements of distance in science. There is a basic distinction between measurement and counting. The result of counting is exact because it involves discrete entities that are not subdivided into fractions. Measurement, on the other hand, involves entities that may be subdivided into smaller and smaller fractions and is thus always an estimate. This distinction between measurement and counting seems, on the surface, to break down at the atomic level, where the quantum theory reveals that not only mass (in the form of elementary particles and atoms) but also many other quantities occur only in discrete units, or quanta. It would seem, therefore, that one could, in theory, reduce measurement to counting at this level. However, the quantum theory also places limitations on the possibility of counting, stressing such concepts as the wavelike nature and indistinguishability of particles and proposing the uncertainty principle as an absolute limitation on certain pairs of related measurements.

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