Three readings are 4.1, 4.3 and 4.5. What is the uncertainty in their mean?

0.2. Half the range: (4.5 − 4.1) ÷ 2.

What is the resolution of a micrometer?

0.01 mm. It is used for small things like the diameter of a wire.

A balance reads 0.3 g when there is nothing on it. What kind of error does this cause?

a systematic error. Every reading is too big by the same amount.

Which is the best way to find the thickness of one sheet of paper?

Measure the thickness of 100 sheets and divide by 100. The percentage uncertainty in the thicker stack is far smaller.

Uncertainty in a measurement · Edexcel IAL Physics revision

In plain words

Every instrument has a limit to how finely it can read, and every time you repeat a measurement you get a slightly different answer. An uncertainty is an honest statement of how far out your value might be. There are two quick rules for estimating one.

5 things to know

The resolution of an instrument is the smallest change it can show: 1 mm for a ruler, 0.1 mm for vernier calipers, 0.01 mm for a micrometer.
For a single reading, take the uncertainty as half the resolution of the instrument.
For repeated readings, take the mean as the best value and half the range (the largest minus the smallest, divided by two) as the uncertainty.
Percentage uncertainty = uncertainty ÷ value × 100%. A small quantity measured with a coarse instrument has a large percentage uncertainty.
Accurate means close to the true value. Precise means repeated readings are close to each other. A systematic error shifts every reading the same way; a random error scatters them.

Worked example

A student measures the diameter of a wire five times with a micrometer: 0.52, 0.54, 0.53, 0.51 and 0.55 mm. Find the mean, its uncertainty and the percentage uncertainty.

Mean = (0.52 + 0.54 + 0.53 + 0.51 + 0.55) ÷ 5 = 0.53 mm.
Uncertainty = half the range = (0.55 − 0.51) ÷ 2 = 0.02 mm.
Percentage uncertainty = 0.02 ÷ 0.53 × 100 = 4%.

Tips and tricks

Quote an uncertainty to one significant figure, and the value to the same decimal place: 0.53 ± 0.02 mm.
To cut a percentage uncertainty, measure something bigger (time twenty swings, not one) or use an instrument with a finer resolution.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Uncertainty in a measurement: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

An instrument has a resolution of 0.1 mm. What uncertainty should be given for a single reading?
- 0.05 mm (the answer)
- 0.1 mm
- 0.2 mm
- 1 mm
Half the resolution.
Three readings are 4.1, 4.3 and 4.5. What is the uncertainty in their mean?
- 0.1
- 0.2 (the answer)
- 0.4
- 4.3
Half the range: (4.5 − 4.1) ÷ 2.
What is the resolution of a micrometer?
- 0.01 mm (the answer)
- 0.1 mm
- 1 mm
- 1 cm
It is used for small things like the diameter of a wire.
A balance reads 0.3 g when there is nothing on it. What kind of error does this cause?
- a systematic error (the answer)
- a random error
- no error
- an error that averages out
Every reading is too big by the same amount.
Which is the best way to find the thickness of one sheet of paper?
- Measure the thickness of 100 sheets and divide by 100. (the answer)
- Measure one sheet with a ruler.
- Estimate it by eye.
- Measure one sheet many times with a ruler.
The percentage uncertainty in the thicker stack is far smaller.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

4 questions, 9 marks. Write your answers on paper, then check them.

Uncertainty in a measurement

Edexcel International A Level Physics WPH · 9 marks · papermunch.org

Name ______________________________ Date ______________

A length of 84 mm is measured once with a ruler of resolution 1 mm. Find the uncertainty and the percentage uncertainty.[2]
Show answerHide answer
± 0.5 mm, which is 0.6%.
I got this one
The time for 10 oscillations is measured three times: 12.4 s, 12.6 s and 12.8 s. Find the period and its uncertainty.[3]
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1.26 ± 0.02 s. The mean is 12.6 s with an uncertainty of half the range, 0.2 s, and both are divided by 10.
I got this one
Explain why timing 20 oscillations instead of one gives a smaller percentage uncertainty in the period.[2]
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The uncertainty in the timing (mostly reaction time) is about the same, but the time measured is 20 times longer, so the uncertainty is a much smaller fraction of it.
I got this one
State the difference between accuracy and precision.[2]
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An accurate result is close to the true value. A precise set of readings are close to one another, whether or not they are close to the true value.
I got this one

Answers: Uncertainty in a measurement

1. ± 0.5 mm, which is 0.6%.
2. 1.26 ± 0.02 s. The mean is 12.6 s with an uncertainty of half the range, 0.2 s, and both are divided by 10.
3. The uncertainty in the timing (mostly reaction time) is about the same, but the time measured is 20 times longer, so the uncertainty is a much smaller fraction of it.
4. An accurate result is close to the true value. A precise set of readings are close to one another, whether or not they are close to the true value.