# 11.01 Summary of introduction to measurement theory

• Measurement is the process of quantifying the different properties of an object
• The properties we measure consist of properties which are some combination of the five base dimensions as well as some other dimensionless quantities
• These properties are measured using a standard set of units called SI units
• A measurement is never a single exact value, it consists of a range of values referred to as the uncertainty interval
• The quality of the measurement can be expressed in terms of precision and accuracy
• Precision is determined by the size of the uncertainty interval compared to the nominal measurement value (the value at the centre of the uncertainty interval)
• Accuracy is determined by the size of the error in the measurment compared to the nominal value. (The error is the difference between the true value and the furthest limit of the uncertainty interval.)
• Two types of errors occur, these are random and systematic errors
• Random errors can be reduced by applying statisitcal techniques to values obtained from repeated measurements.
• Systematic errors can be minimised by the use of calibrated measuring instruments and good measuring techniques
• The precision of a measurement affects its accuarcy because it will affect the difference between the true value and the furthest limit of the uncertainty interval
• The precision of a measurent is affected by:
• The resolution of the measuring instrument (but can be further limited by the measuring technique)
• Lack of clearly defined reference points to measure between
• variation in repeated measurements (can be due to measurement techniques or measuring instruments or even variation in the quantity being measured)
• When carrying out a measurement activity it is important to identify which factors are relevant and which are negligable when determining the uncertainty in the measurement value. Good techniques and the use of calibrated test equipment should be used to obtain the best quality measurment possible and the relevant conditions (i.e. those which can affect the measurement value) should also be recorded
• The precision of a measurement can be expressed explicity by clearly stating the uncertainty or implicitly by the number of significant figures used to express the value.
• Scientific notation is the most convenient way to reflect the precision of a measurement.
• There are rules for determining the precision of the result of a calculation. Information can be lost when values with different levels of resolution are combined in a calculation. It is important to perform the different stages of a calcuation in the correct order so that as much information as possible is preserved.