Build SI units and convert prefixes
Recall the five base quantities named in the syllabus, derive compound units and convert metric prefixes without losing powers of ten.
Section 1 · Physical quantities and units
AS Level · Cambridge International Physics 9702, 2025–2027 syllabus, Topic 1. This online sequence supports learning and practice; it does not replace supervised laboratory work, full timed assessment or human subject-teacher review.
Before you begin
- Read a number with its unit and use multiplication, division, powers and right-angled triangles.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the SI base unit of time?
What you will learn
- Recall the syllabus SI base quantity and unit pairs
- Express common derived units in SI base units
- Convert quantities using the named decimal prefixes
Start with the syllabus base quantities
For Topic 1.2, Cambridge names mass (kilogram, kg), length (metre, m), time (second, s), electric current (ampere, A) and temperature (kelvin, K). Use the symbols exactly: upper-case A and K, lower-case kg, m and s.
A derived unit is built by multiplying or dividing base units in the same way as the defining equation. Velocity has unit m s⁻¹; acceleration m s⁻²; force N = kg m s⁻²; energy J = kg m² s⁻²; power W = kg m² s⁻³. Writing the base-unit form exposes what the quantity means dimensionally.
Prefixes are powers of ten
The syllabus prefixes are pico (p, 10⁻¹²), nano (n, 10⁻⁹), micro (μ, 10⁻⁶), milli (m, 10⁻³), centi (c, 10⁻²), deci (d, 10⁻¹), kilo (k, 10³), mega (M, 10⁶), giga (G, 10⁹) and tera (T, 10¹²). Prefix symbols are case-sensitive: m is milli, while M is mega.
Convert the prefix to a power of ten before calculating. For example, 3.0 ms is 3.0 × 10⁻³ s, and 2.5 MW is 2.5 × 10⁶ W. When units are squared or cubed, the conversion factor is squared or cubed too: 1 cm² = 10⁻⁴ m², not 10⁻² m².
Pause and explain
Which base-unit expression is equivalent to one newton?
Worked example
Write 3.6 km h⁻¹ in m s⁻¹.
Show the worked solution
- Convert 3.6 km to 3600 m.
- Convert 1 h to 3600 s.
- Divide 3600 m by 3600 s.
Answer 1.0 m s⁻¹.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A sample has a mass of 4.5 mg. Express this mass in kg.
Give me a hint
Replace milli with 10⁻³, then convert grams to kilograms.
Compare my reasoning
- 4.5 mg = 4.5 × 10⁻³ g.
- 1 g = 10⁻³ kg, so multiply by another 10⁻³.
- Combine the powers of ten.
4.5 × 10⁻⁶ kg.
Look for these in your work
- Both milli-to-gram and gram-to-kilogram factors included
- Final unit is kg
The energy transferred is 0.72 kJ in 30 s. Calculate the power in W and express W in SI base units.
Give me a hint
Convert kilojoules to joules, then divide by time.
Compare my reasoning
- 0.72 kJ = 720 J.
- Power = energy ÷ time = 720/30.
- Use 1 J = kg m² s⁻², so 1 W = 1 J s⁻¹.
24 W = 24 kg m² s⁻³.
Look for these in your work
- Prefix converted to joules
- Power calculated
- W expressed in base units
A square has side length 2.0 cm. Calculate its area in m².
Give me a hint
Convert the side to metres before squaring, or square the centimetre-to-metre factor.
Compare my reasoning
- 2.0 cm = 2.0 × 10⁻² m.
- Area = (2.0 × 10⁻²)² m².
- Square both the number and the conversion factor.
4.0 × 10⁻⁴ m².
Look for these in your work
- Length conversion correct
- Conversion factor squared
- Area unit is m²
Common mistakes
- Confusing milli (m) with mega (M)
- Changing a prefix but leaving the numerical value unchanged
- Forgetting to square a length-conversion factor for area
What can you explain now?
What is the SI base unit of time?
Compare with the explanation
s
The second, symbol s, is the SI base unit of time.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do you derive a unit from an equation, and why is a prefix conversion more than a change in the unit symbol?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.