SI units, prefixes and uncertainties
Every A-level physics paper expects you to handle units and uncertainties without being told how. A handful of rules covers it: break any unit into base units, and combine uncertainties according to how the quantities are combined.
Part 1 of 3: Learn it
In short
- Six SI base units come up at A-level: kg, m, s, A, K and mol.
- Adding or subtracting quantities: add their absolute uncertainties.
- Multiplying or dividing: add percentage uncertainties; raising to a power n: multiply the percentage by n.
Where this is in your specification
Spec points: AQA 7408 3.1.1 and 3.1.2, OCR A H556 2.2, Edexcel 9PH0 Topic 1
| Board | Topic: Measurements, errors and uncertainties |
|---|---|
| AQA 7408 | 3.1 |
| Edexcel 9PH0 | Topic 1 |
| OCR H556 | Module 2 (and 1.1) |
| Higher C857 76 | Units, prefixes and uncertainties |
Base units and derived units
| Quantity | Base unit |
|---|---|
| mass | kilogram, kg |
| length | metre, m |
| time | second, s |
| current | ampere, A |
| temperature | kelvin, K |
| amount of substance | mole, mol |
Every other unit can be written in base units by using an equation it appears in. From F = ma, the newton is kg m s⁻². From W = Fs, the joule is kg m² s⁻². Both sides of a correct equation have the same base units, which is a quick check on any formula.
Prefixes
| Prefix | Symbol | Factor |
|---|---|---|
| tera | T | 10¹² |
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | μ | 10⁻⁶ |
| nano | n | 10⁻⁹ |
| pico | p | 10⁻¹² |
Kinds of uncertainty
- Absolute uncertainty: the ± value with the same units as the measurement, such as 2.40 ± 0.02 m.
- Fractional uncertainty: absolute uncertainty ÷ value.
- Percentage uncertainty: fractional uncertainty × 100.
For a single reading, the uncertainty is often half the smallest division (or the resolution for a digital meter). For repeated readings, half the range is a common estimate.
Combining uncertainties
| Calculation | Rule |
|---|---|
| a + b or a − b | add the absolute uncertainties |
| a × b or a ÷ b | add the percentage uncertainties |
| aⁿ | multiply the percentage uncertainty by n |
Write the newton in SI base units.
Show the answer
kg m s⁻².
Part 2 of 3: See it worked
Worked examples
Example 1
A sheet measures (2.40 ± 0.02) m by (1.20 ± 0.01) m. Find its area with an absolute uncertainty.
- Area = 2.40 × 1.20 = 2.88 m²
- Percentages: 0.02 ÷ 2.40 = 0.83% and 0.01 ÷ 1.20 = 0.83%, total 1.67%
- 1.67% of 2.88 = 0.048
Answer: (2.88 ± 0.05) m².
Example 2
A trolley travels (50.0 ± 0.5) cm in (8.0 ± 0.2) s. Find its mean speed with an uncertainty.
- Speed = 50.0 ÷ 8.0 = 6.25 cm/s
- Percentages: 0.5 ÷ 50.0 = 1% and 0.2 ÷ 8.0 = 2.5%, total 3.5%
- 3.5% of 6.25 = 0.22
Answer: (6.3 ± 0.2) cm/s.
Common mistakes
- Adding absolute uncertainties when two quantities are multiplied.
- Forgetting to double the percentage uncertainty when a quantity is squared.
- Quoting an uncertainty to more significant figures than the value justifies.
- Treating the gram as the SI base unit of mass. It is the kilogram.
A radius has a 2% uncertainty. What is the percentage uncertainty in r²?
Show the answer
4%.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
Write the newton in SI base units.
kg m s⁻².
A radius has a 2% uncertainty. What is the percentage uncertainty in r²?
4%.
Write 450 nm in metres using standard form.
4.5 × 10⁻⁷ m.
Jobs that use this
- Physicist (se abre en otra pestaña)
- Laboratory technician (se abre en otra pestaña)
- Mechanical engineer (se abre en otra pestaña)
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Estos apuntes están en inglés porque siguen los programas de examen del Reino Unido.
Full lessons and marked practice for this course are coming soon to Brainlag Learn. See courses