SCIENCE · INVESTIGATE AND EXPLAIN

Read an instrument with units

Distinguish a physical quantity from its recorded digits.

Learning outcome: Explain how resolution changes a measurement without changing its underlying quantity.

Starting recap

Centimetres and metres are units of length. Resolution is the smallest step an instrument reports.

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Try

A 10 cm reference is read through an instrument that rounds to a chosen increment.

Open the experiment

Predict

Will finer resolution remove a 1 cm offset?

Your prediction and reason

Experiment

Keep offset at 1 cm and compare resolutions 1, 0.5 and 0.1 cm. Read all three observations.

Calibrate a length reading

Worked teaching model · synthetic values · Three programmed deviations of −0.2, 0 and +0.2 cm illustrate repeat readings. They are not random samples. The reference length is exactly 10 cm in this model.

Instrument offset: 1 cm Instrument resolution: 0.5 cm

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Calculated values on the same fixed scale
Row	Quantity	Value (cm)
1	Reading 1	11
2	Reading 2	11
3	Reading 3	11
4	Known reference	10
5	Mean reading	11
6	Offset-corrected mean	10

Mean error: 1.000 cm. Offset correction leaves 0.000 cm error.

Correct each reading by subtracting the offset. Quantization can remain after correction; identical rounded readings do not imply perfect accuracy.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Keep the quantity while changing the unit

A centimetre is one hundredth of a metre. A reference of 10 cm is therefore 0.10 m. A conversion changes the numerical representation, not the object.

Resolution describes the step between reported values. A device reporting in 0.5 cm increments might record 10.5, 11.0 or 11.5 cm; it cannot distinguish every smaller difference. The lab rounds to the nearest supported increment.

For a true reference of 10 cm, an offset of +1 cm and a programmed deviation of −0.2 cm, the unrounded reading is 10.8 cm. At 0.5 cm resolution it rounds to 11.0 cm. A finer display may report 10.8 cm, but neither value is the true 10 cm.

More digits are not better calibration

Resolution concerns distinguishable increments. Accuracy concerns agreement with a suitable reference. Repeatability concerns consistency across readings. They answer different questions.

The three displayed deviations are deliberately programmed. They illustrate the mechanism but do not constitute independent random sampling. You cannot infer an instrument’s real uncertainty from their tiny spread.

Compare two resolutions without changing the offset. Keep units attached to each row and explain which differences arise from rounding. Record the original readings before applying a correction so another learner can inspect your reasoning.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Explain why displaying more digits does not establish accuracy.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Choose evidence that separates explanations Next: Correct an offset without hiding uncertainty

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