Choosing measuring instruments and measuring length
Choose instruments for length, time, volume, mass, weight, temperature, current and voltage by range and resolution, then make reliable length measurements.
On this page
Definitions
Range is the interval of values an instrument can measure. Resolution is the smallest change in reading it displays or distinguishes. A suitable instrument must cover the expected range and resolve the change that matters.
Key ideas
Choosing an instrument
Length is measured in metres, although centimetres and millimetres are often more convenient in practical work. Choose an instrument by:
- range — it must cover the whole measurement;
- required precision — repeated readings must agree closely enough for the task;
- resolution — the smallest scale division or displayed increment must be fine enough;
- shape and access — for example, internal diameter or depth needs suitable caliper jaws or a depth rod.
Finer resolution supports a more precise reading, but it does not by itself guarantee accurate or repeatable results.
| Instrument | Suitable use | Reading increment in the K323 apparatus list |
|---|---|---|
| tape | room dimensions, long or curved lengths | read the scale provided |
| rule or metre rule | straight lengths within its range | commonly millimetre divisions |
| digital caliper | external/internal diameter and depth | 0.01 mm |
| digital micrometer | small thickness or diameter | 0.001 mm |
Always use the scale or display information supplied in the question if it differs from a typical value.
Choosing instruments for other physical quantities
The same decision works beyond length: first check that the instrument can cover the expected value, then decide whether its resolution is fine enough for the change you need to detect.
| Quantity | Suitable instrument | What makes the reading reliable |
|---|---|---|
| time interval | digital stopwatch, electronic timer or light gates | use clear start and stop events; time several repeated events when possible |
| liquid volume | measuring cylinder | keep it upright and read the bottom of a water meniscus at eye level |
| mass | electronic balance | check or set zero; record mass in kg or g, not N |
| weight | spring balance or force sensor | check zero and read the force in N without exceeding the range |
| temperature | laboratory thermometer or temperature probe | immerse the sensor correctly, avoid touching the container and wait for a steady reading |
| current | ammeter | connect in series and start with a suitable range |
| potential difference | voltmeter | connect in parallel across the component and use a suitable range |
For a derived quantity, choose instruments for every measurement in its equation. To determine density, for example, you need mass and volume. A precise mass reading cannot rescue a poor volume measurement, so compare the likely percentage uncertainty of both.
A student wants to measure the changing temperature of 50 cm³ of water every 30 s. Name the instruments for volume, temperature and time, then give one technique that improves each reading.
Show answer
Correct measurement technique
Use the instrument-specific checks below after confirming that the instrument’s range and resolution suit the task.
Tape or rule
- Place the scale alongside and parallel to the length.
- Align one end with an intact zero mark.
- Read with the eye directly above the mark to avoid parallax.
- If the zero end is damaged, record two scale readings and subtract them.
Digital caliper
- Clean and close the jaws, then check or set zero.
- Use the correct jaws or depth rod.
- Hold the object gently and square to the jaws.
- Record the complete display with its unit.
Digital micrometer
- Check the zero before use.
- Place the object between anvil and spindle.
- Use the ratchet or specified constant-force control; do not overtighten.
- Record the complete display with its unit.
Improving small-length measurements
If one item is too thin for a rule, measure a larger total. For example, stack many sheets of paper, measure the stack, then divide by the number of sheets. Ensure the sheets are compressed consistently and count them correctly.
Repeat a reading to check its scatter. For a wire, also measure at different positions and in different orientations to check whether its diameter varies. A mean can describe an average diameter, but it does not make the wire uniform or correct a constant zero error.
Common mistakes
- Choosing the instrument with the smallest scale division without checking that its range fits the object.
- Reading a scale from an angle, which introduces parallax, or measuring from a worn end instead of a labelled mark.
- Reporting more decimal places than the instrument can justify.
Exam tips
- State both why the range is suitable and why the resolution is sufficient.
- Align the object and scale, view normally, repeat the reading and describe how repeats will be combined.
- For a small repeated length such as paper thickness, measure many layers and divide by the counted number.
Worked examples
Worked example 1
Select an instrument
Problem
Choose a suitable instrument for (1) classroom length, (2) coin diameter to 0.01 mm, and (3) fine-wire thickness to 0.001 mm. Justify each choice.
Worked solution
Match the classroom to the range
Method
Choose a tape.Reason
Its range covers a room-length measurement and it can follow the required span.
Working
Classroom length → tape.Match the coin to external jaws and resolution
Method
Choose a digital caliper.Reason
Its external jaws fit the coin and its display resolves 0.01 mm.
Working
Coin diameter → digital caliper.
Match the wire to the finest stated increment
Method
Choose a digital micrometer.Reason
It suits a fine external thickness and displays to 0.001 mm.
Working
Wire thickness → digital micrometer.
Guided practice 2
Read a rule fully
Problem
An object ends exactly at the 12 cm mark on a rule with 1 mm divisions. Choose the correctly recorded length.
Preserve the scale precision
Hints
Hint 1: convert the smallest division
1 mm = 0.1 cm.
Hint 2: retain the final zero
The last recorded digit should represent tenths of a centimetre.
Show full solution
Match decimal place to resolution
Method
Record one decimal place when using centimetres.Reason
The rule’s 1 mm division equals 0.1 cm.
Working
l = 12.0 cm
Spot the mistake 3
Check range before resolution
Learner response
A student chooses a digital micrometer to measure the 1.6 m length of a table because it has the finest resolution. Diagnose the choice.
Choose an instrument that can span the object
Show solution step by step
Test the range first
Method
Reject the micrometer because it cannot span a 1.6 m table.
Reason
Fine resolution is useless when the expected value lies outside the instrument’s range.
Working
Table length → measuring tape.Use sufficient, not maximal, resolution
Method
Choose a tape with divisions appropriate to the required reading.
Reason
The task does not require micrometre-scale changes.Working
Range requirement: at least 1.6 m.
Exam-style question 1
Measure a fine wire with a micrometer
Examination question
Describe how to obtain a reliable diameter for a fine wire using a digital micrometer. [4 marks]
Include zero, force, repeats and recording
Show solution step by step
Prepare and position
2 marksMethod
Check or set zero, then hold the wire square between anvil and spindle.Reason
A zero check controls offset and square alignment measures the diameter rather than a slanted length.Working
Close gently before reading; do not bend the wire.Control force and repeat
2 marksMethod
Use the ratchet, record the complete display, and repeat at several positions before finding a mean.Reason
Controlled gentle force reduces deformation. Repeats show scatter; readings at different positions can also reveal a genuine variation in diameter.Working
d bar = (d₁ + d₂ + … + dₙ)/n
Self-mark with the mark scheme
Compare your response with each mark point. Select a point only when your response contains that evidence.
Self-mark zero checking, positioning/force, complete recording and repeats.
Try it yourself 4
Correct a zero error
Problem
A digital caliper reads + 0.03 mm when closed and 12.34 mm around an object. Find the corrected diameter.
Remove the offset from the observed reading
Hints
Hint 1: interpret the closed reading
The caliper reads too high by 0.03 mm.
Hint 2: remove the excess
Use corrected reading = observed reading − zero error.
Show solution step by step
Write the correction rule
Method
Subtract the signed zero error from the observed reading.Reason
The closed reading shows the instrument adds 0.03 mm to every observation.Working
corrected = observed-zero errorCalculate the corrected diameter
Method
Subtract the positive offset.Reason
This removes the instrument’s over-reading.Working
d = 12.34 mm-(+0.03 mm) = 12.31 mm
Further mistakes to diagnose
- Choosing an instrument only because the object is “small”, without comparing required precision.
- Letting a tape sag or placing a rule at an angle to the measured length.
- Reading a scale from the side.
- Dropping meaningful zeros from a displayed or scale reading.
- Forgetting to zero digital calipers or micrometers.
- Overtightening a micrometer and deforming the object.
The vernier caliper trainer and micrometer screw-gauge trainer give optional practice with analogue scales. The course’s practical work uses the digital instruments above.
Check your understanding
Check your understanding 1: Measure one thin sheet indirectly
A stack of 200 identical sheets is 18.4 mm thick. Estimate the thickness of one sheet.
Show answer
d = (18.4 mm)/200 = 0.0920 mm
Measuring a stack makes the total length large enough to measure more reliably than one sheet. The answer is an estimate because the sheets may be compressed and may not all have exactly the same thickness.
Mind stretchers
Mind stretcher 1: Design a diameter measurementExtension
Explain how to estimate the diameter of a thin wire using only a metre rule and a cylindrical pencil.
Show answer
Wind many touching turns of the wire around the pencil without overlaps. Measure the total width L of N turns, then calculate:
d = L/N
Using many turns reduces the percentage effect of the rule’s reading uncertainty. Repeat with a fresh winding and compare the results.
Syllabus and review details
- SEC G3 Physics 2027 · 2027
Content Structure, PDF page 9; Subject Content, PDF pages 10–28