The International System of Units
The International System Of Units
The International System of Units (SI), from the French Système International d'Unités, is the modern form of the metric system and is the most widely used system of measurement in the world. It provides a standardized way to express physical quantities, ensuring consistency and facilitating scientific and international trade.
The SI system is built upon a foundation of seven base units, each defined in terms of fundamental physical constants. These base units are used to derive all other units in the system.
The Seven SI Base Units
Here are the seven SI base units and the quantities they measure:
| Quantity | SI Base Unit | Symbol | Definition (Conceptual Summary) |
|---|---|---|---|
| Length | Metre | m | The distance travelled by light in vacuum during a time interval of $ 1/299,792,458 $ of a second. |
| Mass | Kilogram | kg | The base unit of mass; it is defined by taking the fixed numerical value of the Planck constant $ h $ to be $ 6.62607015 \times 10^{-34} \, \text{J}\cdot\text{s} $ (joule-second). |
| Electric Current | Ampere | A | The base unit of electric current; it is defined by taking the fixed numerical value of the elementary charge $ e $ to be $ 1.602176634 \times 10^{-19} \, \text{C} $ (coulomb). |
| Thermodynamic Temperature | Kelvin | K | The base unit of thermodynamic temperature; it is defined by taking the fixed numerical value of the Boltzmann constant $ k $ to be $ 1.380649 \times 10^{-23} \, \text{J/K} $. |
| Amount of Substance | Mole | mol | The base unit of amount of substance; it is defined by taking the fixed numerical value of the Avogadro constant $ N_A $ to be $ 6.02214076 \times 10^{23} \, \text{mol}^{-1} $. |
| Luminous Intensity | Candela | cd | The base unit of luminous intensity; it is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency $ 540 \times 10^{12} \, \text{Hz} $ to be $ 683 \, \text{lm/W} $. |
| Time | Second | s | The duration of $ 9,192,631,770 $ periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. |
SI Prefixes
To express very large or very small quantities conveniently, SI uses a system of prefixes. These prefixes are standardized multipliers that can be attached to any SI unit.
| Prefix | Symbol | Factor | Scientific Notation |
|---|---|---|---|
| yotta | Y | $ 10^{24} $ | (septillion) |
| zetta | Z | $ 10^{21} $ | (sextillion) |
| exa | E | $ 10^{18} $ | (quintillion) |
| peta | P | $ 10^{15} $ | (quadrillion) |
| tera | T | $ 10^{12} $ | (trillion) |
| giga | G | $ 10^9 $ | (billion) |
| mega | M | $ 10^6 $ | (million) |
| kilo | k | $ 10^3 $ | (thousand) |
| hecto | h | $ 10^2 $ | (hundred) |
| deca | da | $ 10^1 $ | (ten) |
| deci | d | $ 10^{-1} $ | (tenth) |
| centi | c | $ 10^{-2} $ | (hundredth) |
| milli | m | $ 10^{-3} $ | (thousandth) |
| micro | $ \mu $ | $ 10^{-6} $ | (millionth) |
| nano | n | $ 10^{-9} $ | (billionth) |
| pico | p | $ 10^{-12} $ | (trillionth) |
| femto | f | $ 10^{-15} $ | (quadrillionth) |
| atto | a | $ 10^{-18} $ | (quintillionth) |
| zepto | z | $ 10^{-21} $ | (sextillionth) |
| yocto | y | $ 10^{-24} $ | (septillionth) |
Derived Units
Derived units are formed by combining base units using multiplication, division, and exponentiation. For example:
- Area: $ \text{m}^2 $ (square metre)
- Volume: $ \text{m}^3 $ (cubic metre)
- Velocity: $ \text{m/s} $ (metres per second)
- Acceleration: $ \text{m/s}^2 $ (metres per second squared)
- Force: Newton (N), which is $ \text{kg} \cdot \text{m/s}^2 $
- Energy: Joule (J), which is $ \text{kg} \cdot \text{m}^2/\text{s}^2 $
- Pressure: Pascal (Pa), which is $ \text{N/m}^2 $
Importance of SI Units
The adoption of the SI system offers several advantages:
- Universality: It provides a common language for science, industry, and commerce worldwide.
- Consistency: The system is based on fundamental physical constants, making definitions stable and reproducible.
- Rationality: It is a coherent system, meaning that units are related in simple and logical ways, avoiding arbitrary conversion factors (unlike older systems like the imperial system). For example, there are no conversion factors between metres, kilograms, and seconds.
- Ease of Use: The decimal nature of the system, with prefixes, makes calculations and conversions straightforward.
Most countries have officially adopted the SI system, making it the global standard for scientific and technical communication.