The language of measurement
| English | Chinese | Pinyin |
|---|---|---|
| units | 单位 | dān wèi |
| accuracy | 准确度 | zhǔn què dù |
| precision | 精密度 | jīng mì dù |
| significant figures | 有效数字 | yǒu xiào shù zì |
| uncertainty | 不确定度 | bù què dìng dù |
A number without a unit means nothing
- 4.2 what? Metres, seconds, kilograms? A quantity is a number and a unit, always.
- Units 单位 follow the SI system, and using them correctly is marked in every practical report.
- This unit is short and it is where the easiest marks in the module live.
Accuracy and precision
- Accuracy 准确度 is closeness to the true value. Precision 精密度 is how tightly repeats cluster.
- A measurement can be precise and wrong: a balance reading 2.001, 2.002, 2.001 g on a 1.500 g mass is precise and inaccurate.
- The two words are not interchangeable, and a question offering both is testing exactly that.
A balance reads 2.001, 2.002, 2.001 g for a mass known to be 1.500 g. What is it?
The repeats cluster tightly, and all of them are wrong by the same amount — a systematic error.
Significant figures and uncertainty
- Significant figures report how precisely you actually measured. Copying eight digits off a calculator claims a precision the instrument did not have.
- Uncertainty 不确定度 is the range a value might lie in, written as $12.4 \pm 0.2$ cm.
- Stating it is part of a scientific claim, not an admission of weakness.
You measure 12.4 cm with a millimetre ruler. Why not write 12.437 cm?
The digits you write are a claim about your equipment. Write only the ones you measured.
How do you write a length of 12.4 cm with an uncertainty of 0.05 cm?
Value, uncertainty, unit. Stating the range is part of the claim, not an admission of weakness.
A ruler marked in millimetres.
You read 12.4 cm. The uncertainty is about half a division, so 12.4 ± 0.05 cm.
Writing 12.437 cm because a calculation produced those digits claims a precision the ruler cannot deliver — and a marker reads it as not understanding the instrument.
The digits you write are a claim about your equipment. Write only the ones you measured.
Repeating a measurement many times removes a systematic error.
Repeats reduce random error only. A balance reading high every time still reads high on average.
Precision is about the instrument; accuracy is about the truth. A systematic error — a balance that reads 0.5 g high every time — produces beautifully precise results that are all wrong by the same amount, and only a check against a known standard reveals it.
Explain in one sentence how you would detect a systematic error in a balance.
Example: "Weigh a standard 100 g calibration mass and see whether the balance reads 100 g."
Do not average away a measurement you know was faulty. Repeating a reading reduces random error; it does nothing to a systematic one, and including a known-bad trial makes the mean worse rather than more reliable.