[Combination of various types of uncertainties to obtain the total uncertainty in a measurement].

→ When uncertainties in a single measurement are combined, an uncertainty can be ignored if it is less than one-third of one of the other uncertainties in the measurement.

The following relationship can be used to determine the total uncertainty in a measured value.

$$ \Delta W = \sqrt{\Delta X^2 \space + \space \Delta Y^2 \space + \space \Delta Z^2} $$

[Combination of uncertainties in measured values to obtain the total uncertainty in a calculated value].

→ When uncertainties in measured values are combined, a fractional/percentage uncertainty in a measured value can be ignored if it is less than one third of the fractional/percentage uncertainty in another measured value.

The following relationship can be used to determine the total uncertainty in a value calculated from the product or quotient of measured values.

$$ \dfrac{\Delta W}{W}=\sqrt{(\dfrac{\Delta X}{X})^2\space + \space (\dfrac{\Delta Y}{Y})^2\space + \space (\dfrac{\Delta Z}{Z})^2} $$

The following relationship can be used to determine the uncertainty in a value raised to a power.

$$ (\dfrac{\Delta W^n}{W^n})=n(\dfrac{\Delta W}{W}) $$

[Use of error bars to represent absolute uncertainties on graphs].

[Estimation of uncertainty in the gradient and intercept of the line of best fit on a graph].

The accuracy of a measurement compares how close the measurement is to the ‘true’ or accepted value.

The uncertainty in a measurement gives an indication of the precision of the measurement.