Measurements and their Errors
SI Units, Prefixes and Estimation
OxfordAQA International AS and A-level Physics
Base quantities and units
| Base quantity | Base unit | Symbol |
|---|---|---|
| Mass | kilogram | kg |
| Length | metre | m |
| Time | second | s |
| Amount of substance | mole | mol |
| Temperature | kelvin | K |
| Current | ampere | A |
Method: a derived unit in base units
- Write a defining equation of the quantity, such as work = force × distance.
- Replace every derived unit by base units: the newton is kg m s−2.
- Collect the powers of each base unit.
| Quantity | Base units |
|---|---|
| Work done, energy | kg m2 s−2 |
| Power | kg m2 s−3 |
| Spring constant | kg s−2 |
| Young modulus | kg m−1 s−2 |
| Magnetic flux density | kg A−1 s−2 |
Base units contain only kg, m, s, mol, K and A.
Writing units
- Write every unit symbol in its own case: kg, m and s lower case; K and A capitals. Write a unit with negative indices, such as J kg−1 K−1.
- Kelvin is K. Never write °K or k for kelvin, and never write °C for a temperature in K.
- The kelvin metre is K m. Never write K M, k m or k M for the kelvin metre.
- Give the named unit (T, Pa, J) unless the base units are asked for.
Prefixes
| Prefix | Symbol | Value |
|---|---|---|
| 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 |
| femto | f | 10−15 |
The prefix on the unit matches the power of ten in the number written beside it.
Converting energy units
electron volt to joule1 eV = 1.60 × 10−19 J
mega electron volt to joule1 MeV = 1.60 × 10−13 J
kilowatt hour to joule1 kW h = 3.6 × 106 J
MeV to J: multiply by 1.60 × 10−13. J to MeV: divide by it.
| Quantity | Symbol | Unit |
|---|---|---|
| Energy | E | J, eV, kW h |
Estimation and orders of magnitude
- Give each input a sensible value from everyday experience, then use the physics equation to reach the derived estimate.
- Convert a temperature in °C to K before using it in an equation.
- Give an estimate to 1 or 2 significant figures.
- An order of magnitude is the power of ten alone, 10n, consistent with the unit stated.
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