When you measure a table with a metre rule marked in millimetres, the smallest division is 1 mm, so you can sensibly write 85.4 cm but not 85.4231 cm. The digits you record are a statement about how sure you are.
Significant figures are the digits known reliably plus one estimated digit. A ruler reading to the nearest millimetre is trustworthy to about the last millimetre; a vernier caliper resolves finer, so it justifies one more figure. Extra digits copied from a calculator carry no real information.
If you divide a distance of 100 m by a time of 9.6 s (2 significant figures), the speed should be quoted to 2 significant figures, because an answer cannot be more precise than the least precise measurement used.
In SPM you are expected to give answers to a sensible number of significant figures, especially in data-based and experiment questions.
Common misconceptions
- More decimal places always means a more accurate answer -> No; precision is limited by the instrument, and extra digits can be meaningless.
- Zeros never count as significant figures -> Zeros between non-zero digits, and trailing zeros after a decimal point, are significant.
- You should round at every step -> Rounding too early builds up error; keep extra digits while working and round only the final answer.
The physics behind it
A significant figure is any digit that carries real information about a measurement: all non-zero digits, any zeros between them, and trailing zeros written after a decimal point. The number of significant figures reports the precision of a measured quantity, whether that is a length in metres (m), a mass in kilograms (kg) or a time in seconds (s).
The key rule for calculations is that a result cannot be more precise than the data it comes from. When you multiply or divide, the answer keeps as many significant figures as the least precise measurement used.
Density shows this cleanly, since ρ = m/V.
Suppose a metal block has mass m = 24.0 g (3 significant figures) and volume V = 3.0 cm³ (2 significant figures). Then:
ρ = m/V = 24.0 g ÷ 3.0 cm³ = 8.0 g cm⁻³
The calculator shows 8, but the volume is only known to 2 significant figures, so the density is written as 8.0 g cm⁻³ (2 significant figures), not 8.00000 g cm⁻³. Every quantity, including the final answer, carries its unit.
See it in everyday life
Look at a digital clinical thermometer that reads 37.0 °C. That final zero is not decoration; it tells you the instrument resolved the temperature to the nearest 0.1 °C and that the tenths digit was genuinely zero.
Writing 37 °C instead would quietly throw away information, suggesting you only measured to the nearest whole degree.
The same care matters at a fuel station. If the pump delivers 30.00 litres, the two zeros after the decimal point say the meter is trusted to the nearest hundredth of a litre.
A hand-dipped measuring can that reads only to the nearest litre could honestly claim 30 litres, but never 30.00 litres.
So the digits you keep are a promise about the tool you used. A tailor measuring cloth with a soft tape marked in centimetres should record 1.5 m, not 1.5000 m, because the extra zeros would claim a precision the tape cannot deliver.
Reading the digits on any everyday display therefore tells you how finely that device can actually measure.
How this comes up in SPM
In Paper 2 this idea is examined with command words such as state the number of significant figures in a reading, write or express a value to a stated number of significant figures, and calculate a quantity and give the answer to a sensible precision. Data-based and experiment questions expect the final answer to match the precision of the raw readings.
Within the Measurement chapter, significant figures sit next to several neighbouring standards. They connect to units and prefixes, since converting between millimetres and metres must not invent or lose digits.
They link to accuracy, consistency and sensitivity of instruments, because the smallest division sets how many figures you may honestly quote. They also relate to random and systematic errors and to the scientific-investigation skills of tabulating and analysing data.
A common way to relate the ideas is to explain why a value copied straight from a calculator display should be rounded before it is recorded. Practising this on your own measurements builds the habit the chapter is testing.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)