• There is always a degree of uncertainty when measurements are taken; the uncertainty can be thought of as the difference between the?actual?reading taken (caused by the equipment or techniques used) and the?true?value
• Uncertainties are?not?the same as errors
  • Errors can be thought of as issues with equipment or methodology that cause a reading to be different from the true value
  • The uncertainty is a range of values around a measurement within which the true value is expected to lie, and is an?estimate

   

• For example, if the true value of the mass of a box is 950 g, but a systematic error with a balance gives an actual reading of 952 g, the uncertainty is ±2 g
• These uncertainties can be represented in a number of ways:
  • Absolute Uncertainty:?where uncertainty is given as a fixed quantity
  • Fractional Uncertainty:?where uncertainty is given as a fraction of the measurement
  • Percentage Uncertainty:?where uncertainty is given as a percentage of the measurement

   

• To find uncertainties in different situations:
• The uncertainty in a reading:?± half the smallest division
• The uncertainty in a measurement:?at least ±1 smallest division
• The uncertainty in repeated data:?half the range i.e. ± ? (largest - smallest value)
• The uncertainty in digital readings:?± the last significant digit unless otherwise quoted

How to calculate absolute, fractional and percentage uncertainty

• Always make sure your absolute or percentage uncertainty is to the same number of?significant figures?as the reading

• When combining uncertainties, the rules are as follows:

Adding / Subtracting Data

• Add?together the absolute uncertainties

Multiplying / Dividing Data

• Add?the percentage or fractional uncertainties

Raising to a Power

• Multiply?the percentage uncertainty by the power

1. Calculate the mean?value

2. Calculate half the range (this is the uncertainty for multiple readings)

3. Calculate percentage uncertainty