measurements and their errors

• A physical quantity is a physical property that can be measured
• A unit is a quantity or amount used as a standard measurement
• SI base units are: kilogram, metre, second, ampere, kelvin, and mole.
• standard prefixes are: femto (10^-15) pico (10^-12) nano (10^-9) micro (10^-6) milli (10^-3) kilo (10^ 3) mega (10^ 6) giga (10^ 9) tera (10^ 12)
• Accuracy: a measurement result is considered accurate if judged to be close to the true value
• True Value: this is the value that would be obtained in an ideal measurement
• Validity: suitability of the investigative procedure to answer the question being asked
• Repeatable: a measurement is repeatable if the original experimenter repeats the investigation using the same method and equipment and obtains the same results
• Reproducible: a measurement is reproducible if the investigation is repeated by another person, or by using different equipment or techniques and the same results are obtained
• Random error: these cause readings to be spread about the true value, due to results varying in an unpredictable way from one measurement to the next
• Systematic error: these cause readings to differ from the true value by consistent amount each time a measurement is made. sources of systematic error can include the environment, methods of observation or instruments used
• Precision: precise measurements are ones in which there is very little spread about the mean value
• Resolution: this is the smallest change in the quantity being measured (input) of measuring instrument that gives a perceptible change in the reading
• order of magnitude is the quantity of powers of 10 that there are in a number, or the number of powers of 0.1 in a negative number
• uncertainty is the interval within which the true value can be expected to lie, with a given level of confidence or probability
• for readings (one judgement), generally: the absolute uncertainty is half the smallest division that the equipment can measure, in either direction
• absolute uncertainties are stated to one significant figure
• for measurements (two judgements), generally, the absolute uncertainty is the smallest division that the equipment can measure
• percentage uncertainty is the (absolute) uncertainty given as a percentage of the measurement

  $εa=$$Δa/a *$$100$
• the uncertainty in a given value is assumed to be +/- 1 in the last significant digit
• if measurements are repeated, the uncertainty can be calculated by finding half the range of the measured values
• adding or subtracting uncertainties.

  add the absolute uncertainties.$Δa=$$Δb+$$Δc$
• when multiplying or dividing uncertainties

  add the percentage uncertainties

  $εa=$$εb+$$εc$
• when combining uncertainties with powers

  multiply the percentage uncertainty by the power

  $εa =$$c*$$εb$
• the vernier calliper is a precise measuring instrument, with a scale that can be read to 0.1 mm
• the micrometer is a precise measuring instrument, with a scale that can be read to 0.01 mm