Lesson 1 · Practical skills

📏 Measurement, Uncertainty & Errors

No measurement is perfect. Scientists report both a value and how far they trust it, and the AS practical exams test exactly that skill.

🎯 Types of error

Random errors scatter readings around the true value and are reduced by repeating and averaging. Systematic errors shift every reading the same way (a zero error, a miscalibrated meter) and are not reduced by averaging. Accurate means close to the true value; precise means readings agree with each other.

Absolute uncertainty: 20.0 ± 0.2 cm Percentage uncertainty = 0.2 ÷ 20.0 × 100 = 1% Mean of 4.1, 4.3, 4.2 = 4.2 uncertainty ≈ half the range = 0.1

🖼️ See it

Random and systematic errorsRandom errorReadings scatter around the truevalueCaused by judgement, noise,parallaxReduced by repeating and averagingSystematic errorEvery reading is shifted the samewayCaused by zero error, faultycalibrationNot reduced by averaging
Precise means the readings agree with each other; accurate means they are close to the true value.
Combining uncertaintiesWhen you…Combine by…add or subtractadding absolute uncertaintiesmultiply or divideadding percentage uncertaintiesraise to a power nmultiplying the % uncertainty by n
Example: radius ± 3% gives area (πr²) ± 6%.

🧮 Combining uncertainties

Adding or subtracting quantities: add the absolute uncertainties. Multiplying or dividing: add the percentage uncertainties. For a power, multiply the percentage uncertainty by the power.

(12.0 ± 0.1) + (8.0 ± 0.2) = 20.0 ± 0.3 4.0 ± 0.1 is 2.5%, 5.0 ± 0.1 is 2% area = 20 with 4.5% uncertainty = 20 ± 0.9 radius ± 3% → area (r²) ± 6%
Give an answer with the same number of decimal places as its uncertainty.
✏️ Quick check · 1 of 8
Error type

A balance that reads 0.3 g with nothing on it causes a:

Same shift each time.
✏️ Quick check · 2 of 8
Reducing error

Repeating readings and averaging mainly reduces:

Scatter.
✏️ Quick check · 3 of 8
Accuracy

A set of readings very close to each other but far from the true value is:

Closeness to each other.
✍️ Type your answer · 4 of 8

Length = 20.0 ± 0.2 cm.

What is the percentage uncertainty?

Enter an exact answer, without rounding.
%
Absolute ÷ value × 100.
✍️ Type your answer · 5 of 8

A reading of 5.0 ± 0.1 A.

What is the percentage uncertainty?

Enter an exact answer, without rounding.
%
Absolute ÷ value × 100.
✍️ Type your answer · 6 of 8

(12.0 ± 0.1) cm and (8.0 ± 0.2) cm are added.

What is the absolute uncertainty in the total, in cm?

Enter an exact answer, without rounding.
cm
Add the absolute uncertainties.
✍️ Type your answer · 7 of 8

A rectangle is 4.0 ± 0.1 by 5.0 ± 0.1.

What is the percentage uncertainty in its area?

Enter an exact answer, without rounding.
%
Add the percentage uncertainties.
✍️ Type your answer · 8 of 8

The radius of a circle has an uncertainty of 3%.

What is the percentage uncertainty in its area (πr²)?

Enter an exact answer, without rounding.
%
Multiply by the power.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5

Absolute uncertainty has the same units as:

Question 2 of 5

For a quantity found by division, uncertainties are combined by adding:

Question 3 of 5

A zero error on a micrometer is a:

Question 4 of 5

The best way to reduce the effect of random error is to:

Question 5 of 5

Which instrument typically has the smallest uncertainty?

Final Challenge

🏆 8-Question Challenge Quiz

Questions from every topic in this course. Pick an answer for each one, then hit Check My Answers.

0 / 8
💪 Keep practicing — go back through the lessons and retake the quiz!
Q1 · Measurement, Uncertainty & Errors

A cube’s side has an uncertainty of 2%. The uncertainty in its volume is:

Q2 · Measurement, Uncertainty & Errors

Random errors can be reduced by:

Q3 · Measurement, Uncertainty & Errors

A systematic error:

Q4 · Measurement, Uncertainty & Errors

A ruler marked in millimetres has an absolute uncertainty of about:

Q5 · Measurement, Uncertainty & Errors

A length is 20.0 ± 0.2 cm. The percentage uncertainty is:

Q6 · Measurement, Uncertainty & Errors

When two measurements are multiplied, their percentage uncertainties are:

Q7 · Measurement, Uncertainty & Errors

Precise readings are:

Q8 · Measurement, Uncertainty & Errors

The SI base unit of mass is the: