Seven base quantities: length (m), mass (kg), time (s), current (A), temperature (K), amount of substance (mol), luminous intensity (cd). Derived units (force, pressure, energy, power, etc.) and prefixes (k, M, μ, n…) for multiples and sub-multiples. Dimensional analysis checks equation correctness; significant figures and order of magnitude for reporting and estimation.
1. Fundamental / Base quantities (SI)
| No. | Physical quantity | Symbol | SI unit | Unit symbol | Dimension |
|---|---|---|---|---|---|
| 1 | Length | l, x | metre | m | [L] |
| 2 | Mass | m | kilogram | kg | [M] |
| 3 | Time | t | second | s | [T] |
| 4 | Electric current | I | ampere | A | [I] |
| 5 | Thermodynamic temperature | T | kelvin | K | [Θ] |
| 6 | Amount of substance | n | mole | mol | [N] |
| 7 | Luminous intensity | Iᵥ | candela | cd | [J] |
2. Derived quantities (common)
| Quantity | Formula | SI unit | Dimension |
|---|---|---|---|
| Area | length × length | m² | [L²] |
| Volume | length³ | m³ | [L³] |
| Velocity | displacement / time | m/s | [LT⁻¹] |
| Acceleration | velocity / time | m/s² | [LT⁻²] |
| Force | mass × acceleration | N (kg·m/s²) | [MLT⁻²] |
| Pressure | force / area | Pa (N/m²) | [ML⁻¹T⁻²] |
| Work / Energy | force × distance | J (N·m) | [ML²T⁻²] |
| Power | work / time | W (J/s) | [ML²T⁻³] |
| Momentum | mass × velocity | kg·m/s | [MLT⁻¹] |
| Frequency | 1 / period | Hz (s⁻¹) | [T⁻¹] |
| Electric charge | current × time | C (A·s) | [IT] |
3. SI prefixes (multiples & sub-multiples)
| Prefix | Symbol | Power of 10 | Example |
|---|---|---|---|
| yotta | Y | 10²⁴ | — |
| zetta | Z | 10²¹ | — |
| exa | E | 10¹⁸ | — |
| peta | P | 10¹⁵ | — |
| tera | T | 10¹² | THz |
| giga | G | 10⁹ | GB |
| mega | M | 10⁶ | MW |
| kilo | k | 10³ | kg |
| hecto | h | 10² | — |
| deca | da | 10¹ | — |
| deci | d | 10⁻¹ | dm |
| centi | c | 10⁻² | cm |
| milli | m | 10⁻³ | ms |
| micro | μ | 10⁻⁶ | μm |
| nano | n | 10⁻⁹ | nm |
| pico | p | 10⁻¹² | ps |
| femto | f | 10⁻¹⁵ | fm |
| atto | a | 10⁻¹⁸ | — |
Unit converter (practical units)
Convert between SI and common practical units
Significant figures
Count sig figs or round to n significant figures
5. Significant figures rules (reference)
| Rule | Example | Sig figs |
|---|---|---|
| All non-zero digits are significant | 123.45 | 5 |
| Zeros between non-zero digits | 1002 | 4 |
| Leading zeros are not significant | 0.0025 | 2 |
| Trailing zeros in whole number (no decimal) | 1200 | Ambiguous (2 or 4) |
| Trailing zeros after decimal | 1200.0 | 5 |
| Scientific notation | 1.200×10³ | 4 |
| Add/Subtract → result has least decimal places. Multiply/Divide → result has least significant figures. | ||
Order of magnitude & estimation
Power of 10 when expressed in scientific notation (e.g. 450 → 2, 0.0032 → −3)
6. Practical units (value in SI)
| Quantity | Unit | Value in SI | Use case |
|---|---|---|---|
| Length | Ångstrom (Å) | 10⁻¹⁰ m | Atomic distances |
| Length | Fermi (fm) | 10⁻¹⁵ m | Nuclear physics |
| Length | Astronomical unit (AU) | ≈ 1.496×10¹¹ m | Solar system |
| Length | Light-year | 9.46×10¹⁵ m | Interstellar |
| Mass | Atomic mass unit (u) | 1.66054×10⁻²⁷ kg | Atomic/molecular |
| Pressure | Atmosphere (atm) | 1.01325×10⁵ Pa | Atmospheric |
| Pressure | mm of Hg (torr) | 133.322 Pa | Blood pressure, vacuum |
| Energy | Electronvolt (eV) | 1.602×10⁻¹⁹ J | Atomic & particle physics |
4. Dimensional analysis (summary)
| Purpose | Method |
|---|---|
| Check correctness | Both sides of equation must have same dimensions |
| Derive relation | Assume quantity ∝ product of powers of base quantities |
| Convert units | Use conversion factors (1 unit = x another) |
| Limitations | Cannot find dimensionless constants, trig or exponential |
Dimensionless: coefficient of friction (μ), Reynolds number (Re), Mach number, refractive index (n), Poisson's ratio (ν), angle (radian), strain.
About units and measurement
The SI has seven base quantities; all others are derived. Dimensional analysis checks that equations are dimensionally consistent and helps convert units. Significant figures reflect precision: in multiplication/division use the least number of sig figs; in addition/subtraction use the least decimal places. Order of magnitude is the power of 10 when the quantity is written in scientific notation (e.g. 450 → 4.5×10² → order 2).
Sig fig rules (short)
Non-zero digits are significant; zeros between non-zero digits are significant; leading zeros are not; trailing zeros after a decimal are significant; trailing zeros in a whole number without a decimal can be ambiguous. Use scientific notation (e.g. 1.200×10³) to show four significant figures.