3.1 KiB
SL Physics
The course code for this page is SPH3U7.
1.1 - Measurements in physics
Fundamental units
Every other SI unit is derived from fundamental units. Memorise these!
| Quantity type | Unit | Symbol |
|---|---|---|
| Time | Second | s |
| Distance | Metre | m |
| Mass | Kilogram | kg |
| Electric current | Ampere | A |
| Temperature | Kelvin | K |
| Amount of substance | Mole | mol |
| Luminous intensity | Candela | cd |
Metric prefixes
Every SI unit can be expanded with metric prefixes.
!!! example milli + metre = millimetre (\(10^{-3}\)) m
| Prefix | Abbreviation | Value | Inverse (\(10^{-n}\)) abbreviation | Inverse prefix |
|---|---|---|---|---|
| deca- | da | \(10^1\) | d | deci- |
| hecto- | h | \(10^2\) | c | centi- |
| kilo- | k | \(10^3\) | m | milli- |
| mega- | M | \(10^6\) | µ | micro- |
| giga- | G | \(10^9\) | n | nano- |
| tera- | T | \(10^{12}\) | p | pico- |
| peta- | P | \(10^{15}\) | f | femto- |
| exa- | E | \(10^{18}\) | a | atto- |
Significant figures
- The leftmost non-zero digit is the most significant digit.
- If there is no decimal point, the rightmost non-zero digit is the
least significant digit.
- Otherwise, the right-most digit (including zeroes) is the least significant digit.
- All digits between the most and least significant digits are significant.
- Pure (discrete) numbers are unitless and have infinite significant figures.
!!! example In \(123000\), there are
3 significant digits.
In \(0.1230\), there are 4 significant
digits.
- When adding or subtracting significant figures, the answer has the same number of decimals as the number with the lowest number of decimal points.
- When multiplying or dividing significant figures, the answer has the same number of significant figures as the number with the lowest number of significant figures.
- Values of a calculated result can be no more precise than the least precise value used.
!!! example \[1.25 + 1.20 = 2.45\] \[1.24 + 1.2 = 2.4\] \[1.2 × 2 = 2\] \[1.2 × 2.0 = 2.4\]
!!! warning When rounding an answer with significant figures, if the least significant figure is \(5\), round up only if the second-least significant figure is odd.
$$1.25 + 1.2 = 2.4$$
$$1.35 + 1.2 = 2.6$$Scientific notation
Scientific notation is written in the form of \(m×10^{n}\), where \(1 \leq m < 10, n \in \mathbb{Z}\). All
digits before the multiplication sign in scientific notation are
significant.
!!! example The speed of light is 300 000 000 ms-1, or \(3×10^8\) ms-1.
Orders of magnitude
The order of magnitude of a number can be found by converting it to scientific notation and taking its power of 10.
!!! example - The order of magnitude of 212000, or \(2.12×10^{5}\), is 5. - The order of magnitude of 0.212, or \(2.12×10^{-1}\), is -1.