Precision

Examples of Precision in the following topics:

• Accuracy, Precision, and Error

  • Accuracy is how closely the measured value is to the true value, whereas precision expresses reproducibility.
  • Measurements can be both accurate and precise, accurate but not precise, precise but not accurate, or neither.
  • This is an easy to understand introduction to accuracy and precision.
  • On this bullseye, the hits are all close to the center, but none are close to each other; this is an example of accuracy without precision.
  • Describe the difference between accuracy and precision, and identify sources of error in measurement

• Significant Figures

  • Significant figures are digits which contribute to the precision of a number.
  • Significant figures of a number are digits which contribute to the precision of that number.
  • Numbers that do not contribute any precision and should not be counted as a significant number are:
  • This convention clarifies the precision of such numbers.
  • For example, if a measurement that is precise to four decimal places (0.0001) is given as 12.23, then the measurement might be understood as having only two decimal places of precision available.

• The Uncertainty Principle

  • In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position (x) and momentum (p), can be known simultaneously.
  • The more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.

• High Resolution Spectra

  • Tables of precise mass values for any molecule or ion are available in libraries; however, the mass calculator provided below serves the same purpose.

• Exact Numbers

  • When mass is reported as 0.5237 g, as shown on this scale, it is more precise than a mass reported as 0.5 g.

• Major Features of a Phase Diagram

  • Although phases are conceptually simple, they are difficult to define precisely.

• Molecules

  • The full elemental composition of a molecule can be precisely represented by its molecular formula, which indicates the exact number of atoms that are in the molecule.

• Indeterminacy and Probability Distribution Maps

  • Quantum indeterminacy can be illustrated in terms of a particle with a definitely measured momentum for which there must be a fundamental limit to how precisely its location can be specified.
  • For example, a particle with a definitely measured energy has a fundamental limit to how precisely one can specify how long it will have that energy.

• Acid-Base Titrations

  • An acid-base titration is an experimental procedure used to determined the unknown concentration of an acid or base by precisely neutralizing it with an acid or base of known concentration.
  • This is the first titration and it is not very precise; it should be excluded from any calculations.

• Bond Lengths

  • X-ray diffraction of molecular crystals allows for the determination of the three-dimensional structure of molecules and the precise measurement of internuclear distances.