The big idea: Before any calculation you have to get a good reading. Two habits matter.
The two habits
- Read the scale honestly — look straight on, and check the instrument reads zero before you start
- Pick the right instrument — one whose smallest scale division (its resolution) is fine enough for what you're measuring
- Resolution
- the smallest division an instrument can read — e.g. 1 mm on a metre rule, 0.01 mm on a micrometer. A finer resolution gives a smaller uncertainty.
- Parallax error
- a wrong reading because you looked at the scale from an angle instead of straight on.
- Zero (alignment) error
- the instrument doesn't read zero when it should — every reading is then off by that fixed amount.
Spot it: Read the bottom of the meniscus at eye level for a liquid · check the jaws read 0 before using a caliper · line your eye square to a ruler.
Correcting a zero error: Read the instrument with nothing to measure first. Corrected value = reading − zero reading, keeping the sign.
A caliper reads −0.3 mm when closed and 20.6 mm across a sphere: diameter = 20.6 − (−0.3) = 20.9 mm.
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience — and you can try it with your first topic free to keep:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
Choose the instrument whose resolution is fine enough that the reading isn't dominated by uncertainty — but no finer than you need.
Two examples
- A ruler is fine for a 30 cm pencil.
- A wire's diameter of under a millimetre needs a micrometer.
| Instrument | Smallest division (resolution) | Use it to measure |
|---|---|---|
| Metre rule | 1 mm | lengths from a few cm up to ~1 m |
| Vernier caliper | 0.1 mm | the diameter of a marble or width of a block |
| Micrometer screw gauge | 0.01 mm | the thickness of a wire or a sheet of paper |
| Measuring cylinder | 1 mL (often) | the volume of a liquid |
| Protractor | 1° | an angle (e.g. of refraction) |
| Stopwatch | 0.01 s | a time interval |
Resolution of a digital display: One unit in the last digit shown. A balance reading 1.427 g has a resolution of 0.001 g; a timer reading 2.36 s, 0.01 s.
Rule of thumb: The instrument's resolution should be a small fraction of the quantity you're measuring. Reading a 0.40 mm wire with a 1 mm ruler is useless; a micrometer (0.01 mm) makes the uncertainty about 2.5% instead of over 100%.
You must measure the diameter of a copper wire, expected to be about 0.40 mm. Which instrument should you use, and what is the fractional uncertainty in one reading?
Model answer plan
See the answer broken into clear points, with guidance on how each point earns marks.
See how examiners mark answers
Answer exam-style questions with model answers. Learn exactly what earns marks and what doesn't.
How this is tested: Paper 1B almost always opens by handing you an experiment and asking you to suggest a suitable instrument (1 mark).
Earn the mark: The mark is only awarded if you justify it by its resolution. Naming the instrument alone usually isn't enough.
A student investigates how the resistance of a metal rod depends on its dimensions. The rod is about 25 cm long and about 8 mm in diameter. (a) Suggest a suitable instrument to measure its length and justify your choice. (b) Suggest a suitable instrument to measure its diameter and justify your choice.
Model answer plan
See the answer broken into clear points, with guidance on how each point earns marks.
Sometimes a single reading is too small to measure well, or you can't reach the quantity directly. The fix is to measure a multiple and then divide.
Both the value and its absolute uncertainty get divided by the number of items, so the result is far more precise.
The trick: To get the thickness of one sheet of paper, measure a stack of 100 with a ruler and divide by 100.
To get the period of one swing of a pendulum, time 10 swings with a stopwatch and divide by 10.
- the number of identical items measured together (sheets, swings)
- the absolute uncertainty in the single measurement of the whole stack
A stack of 100 identical sheets of paper measures 9.0 mm with a ruler of resolution 1 mm. Find the thickness of one sheet and its absolute uncertainty.
Model answer plan
See the answer broken into clear points, with guidance on how each point earns marks.
Study smarter, not longer
Most students waste 40% of study time on topics they already know. Our AI tracks your progress and optimizes every minute.
Paper 1B also asks how an experiment was designed: what was changed, what was measured, what was kept the same, and why the readings were taken where they were.
- Independent variable
- the quantity you change on purpose (plotted on the x-axis).
- Dependent variable
- the quantity you measure each time (plotted on the y-axis).
- Control variable
- any other quantity that could change the result, so it is kept the same.
Range and number of readings: Take at least five values of the independent variable, spread across as wide a range as is practical, and repeat each one.
Too small a value gives a reading too small to measure well (a large fractional uncertainty); too large a value can be impractical, or swamped by background effects.
Ways to control variables
- Calibrate the apparatus and sensors; check every meter reads zero first
- Keep the conditions constant: room temperature, no draughts
- Insulate against heat loss or gain
- Reduce friction; keep currents small so wires do not heat up (low-resistance connections)
- Measure the background radiation and subtract it
- Think about safety: hot liquids, high voltages, radioactive sources, lasers
Sensors and video analysis
A sensor with a data logger (force, motion, light, temperature) takes many readings quickly and with no reaction time. A video of a moving object can be stepped through frame by frame: each frame is a known fraction of a second.
A trolley is filmed at 50 frames per second. It moves 6.0 cm in 10 frames. Calculate its speed.
Model answer plan
See the answer broken into clear points, with guidance on how each point earns marks.
Where it shows up: This is the opening data question on Paper 1B.
What they ask
- _Suggest / state_ a suitable instrument — justify it by resolution.
- _State_ one way to avoid a reading error (parallax, zero error).
- _Describe_ a method that reduces the absolute uncertainty (measure a multiple).
- _Identify_ the control variables, or _state_ why one is controlled.
- _Suggest_ why a value is outside a sensible range (too small to measure well, or impractical).
Once you've measured your quantities you usually combine them in a formula — so the data booklet's uncertainty-propagation rules come next. They are given in the booklet, so you can look them up:
- the calculated result (e.g. a density or area)
- the measured quantities you combine
- the absolute uncertainty in a (same unit as a)
- the fractional uncertainty in a (no unit)
- the power a quantity is raised to
Don't mix them up: For adding or subtracting () you add the absolute uncertainties: . This one is derived, not in the booklet — know it from memory. Fractional uncertainties are for × and ÷ only.