Whenever a measurement is made there is always some uncertainty about the…

The idea

Every measurement has uncertainty because instruments have limited resolution, conditions vary and the person reading the scale may make small errors. Uncertainty is the range of values within which the true value is likely to lie. For example, a balance reading to the nearest 0.01 g has an uncertainty of about ±0.01 g, while a thermometer read to the nearest 1 °C has an uncertainty of about ±0.5 °C if you estimate between marks. Uncertainty is not the same as a mistake: it is unavoidable and can be reduced but not removed. Repeating measurements and using finer-scale instruments can reduce uncertainty, and the mean of repeated readings is usually more reliable.

What earns the marks

• State that all measurements have some uncertainty.
• Identify a source of uncertainty, such as instrument resolution or reading the scale.
• Distinguish uncertainty from a mistake or a gross error.
• Explain that repeating measurements or using a finer scale can reduce uncertainty.
• Use the resolution of an instrument to estimate the uncertainty in a single reading.

Common mistakes and how to put them right

• Treating uncertainty as a mistake.

  Put it right by explaining that uncertainty is unavoidable and affects every measurement.

• Believing that a more precise instrument removes uncertainty completely.

  Put it right by stating that it only reduces uncertainty.

• Confusing uncertainty with accuracy.

  Put it right by explaining that uncertainty describes the spread of possible values, while accuracy describes closeness to the true value.

Exam tips

• Quote the instrument resolution when asked to estimate uncertainty.
• Use the phrase true value when defining uncertainty.
• Give a specific example, such as a balance reading to the nearest 0.01 g, rather than a vague statement.