Measurements and their Errors
SI Units, Prefixes and Estimation
AQA 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 the defining equation of the quantity.
- Replace every derived unit by base units: the newton is kg m s−2.
- Collect the powers of each base unit.
| Quantity | Base units |
|---|---|
| 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. Never write N m−1 as the base units of a spring constant.
- Homogeneity: the units on both sides of a physics equation are the same, so an unknown constant takes the units that balance the equation.
Writing units
- Write a unit with negative indices: C kg−1, J kg−1 K−1. Never write a unit with a solidus, C / kg.
- 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 power of ten in a numerical answer matches the prefix on the unit written beside it.
Orders of magnitude and estimation
- Calculate a raw value first, in the unit stated.
- Give the order of magnitude as the power of ten alone, 10n, consistent with the raw value. Never write an order of magnitude written 1.0 × 10n or 2 × 10n.
- The order of magnitude depends on the unit: the power of ten must be consistent with the unit given.
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