1.2+Measurement+and+Uncertainties

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The SI system of fundamental and derived units
State the fundamental units in the SI system. Students need to know the following: kilogram, metre, second, ampere, mole and kelvin. Distinguish between fundamental and derived units and give examples of derived units. Convert between different units of quantities. For example, J and kW h, J and eV, year and second, and between other systems and SI. State units in the accepted SI format. Students should use m s–2 not m/s2 and ms–1 not m/s. State values in scientific notation and in multiples of units with appropriate prefixes. For example, use nanoseconds or gigajoules.

Uncertainty and error in measurement
Describe and give examples of random and systematic errors. Distinguish between precision and accuracy. A measurement may have great precision yet may be inaccurate (for example, if the instrument has a zero offset error). Explain how the effects of random errors may be reduced. Students should be aware that systematic errors are not reduced by repeating readings. Calculate quantities and results of calculations to the appropriate number of significant figures. The number of significant figures should reflect the precision of the value or of the input data to a calculation. Only a simple rule is required: for multiplication and division, the number of significant digits in a result should not exceed that of the least precise value upon which it depends. The number of significant figures in any answer should reflect the number of significant figures in the given data.

State uncertainties as absolute, fractional and percentage uncertainties. Determine the uncertainties in results. A simple approximate method rather than root mean squared calculations is sufficient to determine maximum uncertainties. For functions such as addition and subtraction, absolute uncertainties may be added. For multiplication, division and powers, percentage uncertainties may be added. For other functions (for example, trigonometric functions), the mean, highest and lowest possible answers may be calculated to obtain the uncertainty range. If one uncertainty is much larger than others, the approximate uncertainty in the calculated result may be taken as due to that quantity alone. Identify uncertainties as error bars in graphs. State random uncertainty as an uncertainty range (±) and represent it graphically as an “error bar”. Error bars need be considered only when the uncertainty in one or both of the plotted quantities is significant. Error bars will not be expected for trigonometric or logarithmic functions. Determine the uncertainties in the gradient and intercepts of a straight line graph. Only a simple approach is needed. To determine the uncertainty in the gradient and intercept, error bars need only be added to the first and the last data points.