Choosing a unit means matching a quantity (what you measure) to a unit (the agreed amount you measure it in), and picking one of a sensible size. It appears in almost every calculation in measurement and quantities and in every later topic.
The standard base units used in IGCSE Physics are the metre (m) for length, the kilogram (kg) for mass and the second (s) for time. Check the current Cambridge Physics 0625 syllabus for the exact list of quantities and units your year requires.
How do I pick a sensible unit?
Ask two questions. First, which quantity is this: length, mass, time, volume, speed or something else? Second, what size is it, so that the number is neither tiny nor enormous?
| Quantity | Everyday size | Sensible unit |
|---|---|---|
| Thickness of a coin | about 2 mm | mm |
| Length of a classroom | about 8 m | m |
| Distance between two towns | about 120 km | km |
| Mass of a mango | about 300 g | g |
| Mass of a car | about 1200 kg | kg |
| Time for a 100 m sprint | about 14 s | s |
| Volume of a teaspoon | about 5 cm³ | cm³ or mL |
The sizes in the table are rough everyday estimates to help you judge scale, not exam data.
How do I convert between units?
Use the relationship between the two units and decide whether the number should get bigger or smaller.
- Write the relationship: 1 km = 1000 m, 1 h = 3600 s, 1 g = 0.001 kg.
- Decide the direction. A smaller unit needs a larger number (2 m = 200 cm).
- Multiply or divide by the conversion factor.
- Check the size. Does the final number look reasonable for the object?
For area and volume, the factor is squared or cubed. Since 1 cm = 0.01 m, we have 1 cm² = 0.0001 m² (10⁻⁴ m²) and 1 cm³ = 0.000001 m³ (10⁻⁶ m³).
Worked example
A block is 4.0 cm × 2.5 cm × 10 cm. Give its volume in cm³ and in m³. (Invented example data.)
Step 1, volume in cm³: 4.0 × 2.5 × 10 = 100 cm³.
Step 2, conversion factor: 1 cm³ = 10⁻⁶ m³, because 1 cm = 10⁻² m and (10⁻²)³ = 10⁻⁶.
Step 3, convert: 100 × 10⁻⁶ = 1.0 × 10⁻⁴ m³.
Step 4, size check: a small block should have a tiny volume in m³, and 0.0001 m³ is tiny. This passes.
Answer: 100 cm³ = 1.0 × 10⁻⁴ m³
The mistake to watch for
A common slip is to convert cm³ to m³ by dividing by 100, as if the factor for length applied to volume.
Mistaken answer: 100 cm³ = 1 m³
The student used 1 m = 100 cm once, but volume has three lengths multiplied, so the factor must be used three times.
The correction is to cube the length factor: 100³ = 1 000 000, so divide by 1 000 000. The size check also catches it: 1 m³ is about the volume of a large washing machine, far more than a small block.
Check yourself
1. Choose a sensible unit for each: the mass of a bag of rice, the thickness of a sheet of paper, the time of a school lesson.
Show answer
Bag of rice: kg (or g for a small bag). Thickness of paper: mm (it is a fraction of a millimetre, so a micrometre is also reasonable). School lesson: minutes (or hours), and s for a calculation in SI units.
2. A van travels at 72 km/h. Give this speed in m/s.
Show answer
72 km/h = 72 000 m per 3600 s = 72 000 ÷ 3600 = 20 m/s.
3. A sample has a mass of 350 g. Give this in kg, and state one check that the answer is reasonable.
Show answer
350 ÷ 1000 = 0.35 kg. Check: kilograms are a larger unit, so the number should be smaller than 350, and 0.35 is.
Where this leads next
With units secure, move on to reading an analogue scale with interpolation, then try the measurement and quantities practice set. The bounds and rounding explainer helps when a unit conversion changes how many digits you should keep.
Some students know every equation but lose marks through units and conversions in longer questions. Our teachers look for that pattern in online one-to-one Physics tuition.