Which of these is an SI base unit?

kelvin. The others are built from base units: the coulomb is A s.

What does the prefix giga mean?

10⁹. Kilo, mega, giga, tera go up in thousands.

What is 5.0 µC in coulombs?

5.0 × 10⁻⁶ C. Micro means 10⁻⁶.

An equation is homogeneous. What does that tell you?

Every term has the same units. It could still be out by a numerical factor.

SI units and prefixes · Cambridge A Level Physics revision

In plain words

Every unit in physics can be built from just a handful of base units. That gives you a powerful check: if the units on the two sides of an equation don't match, the equation is wrong.

Three things to know

SI base units: kilogram (kg), metre (m), second (s), ampere (A), kelvin (K), and the mole (mol) for amount of substance. Everything else is derived: the newton is kg m s⁻², the joule is kg m² s⁻².
Prefixes: pico (p) 10⁻¹², nano (n) 10⁻⁹, micro (µ) 10⁻⁶, milli (m) 10⁻³, centi (c) 10⁻², kilo (k) 10³, mega (M) 10⁶, giga (G) 10⁹, tera (T) 10¹².
An equation is homogeneous if every term has the same units. A correct equation must be homogeneous, though a homogeneous one can still be wrong by a number.

Worked example

Find the base units of pressure.

Pressure = force ÷ area.
Force is mass × acceleration: kg m s⁻². Area is m².
kg m s⁻² ÷ m² = kg m⁻¹ s⁻².

Tips and tricks

To find derived units, start from a defining equation you know and replace each quantity with its units.
Convert prefixes before you calculate. 450 nm is 4.5 × 10⁻⁷ m.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

SI units and prefixes: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

Which of these is an SI base unit?
- newton
- joule
- kelvin (the answer)
- coulomb
The others are built from base units: the coulomb is A s.
What does the prefix giga mean?
- 10³
- 10⁶
- 10⁹ (the answer)
- 10¹²
Kilo, mega, giga, tera go up in thousands.
What are the base units of force?
- kg m s⁻¹
- kg m s⁻² (the answer)
- kg m² s⁻²
- kg s⁻²
From F = ma.
What is 5.0 µC in coulombs?
- 5.0 × 10⁻³ C
- 5.0 × 10⁻⁶ C (the answer)
- 5.0 × 10⁻⁹ C
- 5.0 × 10⁶ C
Micro means 10⁻⁶.
An equation is homogeneous. What does that tell you?
- It is certainly correct.
- Every term has the same units. (the answer)
- It has no constants in it.
- It only works for SI units.
It could still be out by a numerical factor.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 6 marks. Write your answers on paper, then check them.

SI units and prefixes

Cambridge International AS & A Level Physics 9702 · 6 marks · papermunch.org

Name ______________________________ Date ______________

Find the base units of energy.[2]
Show answerHide answer
kg m² s⁻². Work = force × distance = kg m s⁻² × m.
I got this one
Show that the equation v² = u² + 2as is homogeneous.[2]
Show answerHide answer
v² and u² have units m² s⁻². 2as has units m s⁻² × m = m² s⁻². Every term has the same units.
I got this one
Write 33 kΩ in ohms and 4.7 µF in farads, in standard form.[2]
Show answerHide answer
3.3 × 10⁴ Ω and 4.7 × 10⁻⁶ F.
I got this one

Answers: SI units and prefixes

1. kg m² s⁻². Work = force × distance = kg m s⁻² × m.
2. v² and u² have units m² s⁻². 2as has units m s⁻² × m = m² s⁻². Every term has the same units.
3. 3.3 × 10⁴ Ω and 4.7 × 10⁻⁶ F.