1.3 AS Level

Errors and uncertainties

8 flashcards to master this topic

Definition Flip

Define 'systematic error' and provide an example.

Answer Flip

A systematic error is a consistent error that affects all readings in the same way, shifting them from the true value in a consistent direction.

Example: A zero error on a measuring instrument.
Definition Flip

Define 'random error' and provide an example.

Answer Flip

A random error is an unpredictable error that affects readings inconsistently, causing them to be scattered around the true value.

Example: Parallax error when reading a scale.
Key Concept Flip

Explain the difference between accuracy and precision.

Answer Flip

Accuracy refers to how close a measurement is to the true value. Precision refers to the repeatability of a measurement; how close multiple measurements are to each other, regardless of the true value.

Key Concept Flip

A voltmeter consistently reads 0.2V too high. What type of error is this, and how does it affect accuracy and precision?

Answer Flip

This is a systematic error (specifically, a zero error). It affects the accuracy of the measurements, making them consistently inaccurate. It does not directly affect the precision, as the measurements are still repeatable with the same offset.

Calculation Flip

How do you combine absolute uncertainties when adding or subtracting measurements?

Answer Flip

When adding or subtracting measurements, the absolute uncertainties are added together. For

Example: If x = a + b, then Δx = Δa + Δb, where Δ represents the absolute uncertainty.
Calculation Flip

How do you combine percentage uncertainties when multiplying or dividing measurements?

Answer Flip

When multiplying or dividing measurements, the percentage uncertainties are added together. For

Example: If x = a * b, then %Δx = %Δa + %Δb, where %Δ represents the percentage uncertainty.
Calculation Flip

A student measures a length as 2.5 ± 0.1 cm and a width as 1.2 ± 0.1 cm. Calculate the area and its absolute uncertainty.

Answer Flip

Area = 2.5 * 1.2 = 3.0 cm². Percentage uncertainty in length = (0.1/2.5)*100 = 4%. Percentage uncertainty in width = (0.1/1.2)*100 = 8.33%. Total percentage uncertainty in area = 4 + 8.33 = 12.33%. Absolute uncertainty in area = (12.33/100) * 3.0 = 0.37 cm². Therefore, area = 3.0 ± 0.4 cm² (rounded to 1 sf).

Key Concept Flip

Describe how repeated measurements can help reduce the impact of random errors.

Answer Flip

Taking multiple measurements and calculating the average helps to reduce the impact of random errors. Random errors tend to cancel each other out when averaged, providing a more accurate estimate of the true value.

Ready to test yourself?

Practice with MCQ questions to check your understanding of Errors and uncertainties.

Take Quiz
1.2 SI units 1.4 Scalars and vectors