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Units and Standards of Measurement01:10

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A physical quantity is defined either by specifying its measurement method or by stating how it is calculated from other measurements. For example, consider a metallic cube. We might define its mass and dimensions by specifying methods for measuring them, such as using a weighing machine and a meter scale. Then, we could define the volume by stating that it is the cube of its side, and we could calculate the density as the mass divided by the volume.
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Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.  Highly accurate...
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Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA
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Mathematics and Measurement.

R F Boisvert1, M J Donahue1, D W Lozier1

  • 1National Institute of Standards and Technology, Gaithersburg, MD 20899-0001.

Journal of Research of the National Institute of Standards and Technology
|August 9, 2016
PubMed
Summary
This summary is machine-generated.

Mathematics is crucial for measurement science at the National Institute of Standards and Technology (NIST). This paper reviews historical contributions and current applications, highlighting future directions in mathematical research for metrology.

Keywords:
deconvolutiondigital librarieshistory of NBSlinear algebramathematical reference datamathematical softwaremicromagnetic modelingparameter estimationscientific computingsoftware testing

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Area of Science:

  • Mathematics and Measurement Science
  • Metrology
  • Applied Mathematics

Background:

  • The National Bureau of Standards (NBS) initiated mathematical work in the 1930s with the Math Tables project.
  • NIST has a long-standing history of integrating mathematical principles into measurement science.
  • Understanding the historical context is key to appreciating current NIST initiatives.

Purpose of the Study:

  • To delineate the integral role of mathematics within NIST's measurement science endeavors.
  • To provide a historical overview of mathematical applications in metrology at NIST.
  • To showcase contemporary and emerging mathematical challenges in measurement science.

Main Methods:

  • Historical review of NIST's mathematical projects.
  • Case studies of recent mathematical applications in measurement science.
  • Analysis of current trends and future outlooks in mathematical metrology.

Main Results:

  • Mathematics has been foundational to NIST's measurement science since the 1930s.
  • Recent applications include solving ill-posed inverse problems and software accuracy characterization.
  • Development and dissemination of mathematical reference data are key NIST contributions.

Conclusions:

  • Mathematics is indispensable for advancing measurement science at NIST.
  • NIST actively applies advanced mathematical techniques to solve complex metrology problems.
  • Future research will focus on emerging mathematical challenges in measurement science.