The big idea: Before any calculation you have to get a good reading. Two habits matter:
- 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.
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Choose the instrument whose resolution is fine enough that the reading isn't dominated by uncertainty — but no finer than you need. 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 |
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?
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How this is tested: Paper 1B almost always opens by handing you an experiment and asking you to suggest a suitable instrument (1 mark) — and 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.
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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.
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Where it shows up: This is the opening data question on Paper 1B:
- _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).
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.