Dimensional Analysis of Quantity
The seven basic quantities lead to a number of derived quantities such as pressure, volume, force, density, speed etc. The units for such quantities can be obtained by defining the derived quantity in terms of the base quantities using the base units. For example, speed (velocity) is expressed in distance/time. So the unit is m/s or ms-1. The unit of force (mass×acceleration) is kgms-2 and the unit for acceleration is ms-2.
Table: Derived Units
Physical quantity | Unit | Symbol |
Area | square metre | m2 |
Volume | cubic metre | m3 |
Velocity | metre per second | ms–1 |
Acceleration | metre per second square | ms–2 |
Density | kilogram per cubic metre | kg m–3 |
Molar mass | kilogram per mole | kg mol–1 |
Molar volume | cubic metre per mole | m3 mol–1 |
Molar concentration | mole per cubic metre | mol m–3 |
Force | newton (N) | kg m s–2 |
Pressure | pascal (Pa) | N m–2 |
Energy work | joule (J) | kg m2 s–2, Nm |
Table: Standard prefixes use to reduce the basic units
| Multiple | Prefix | Symbol | Submultiple | Prefix | Symbol |
| 1024 | yotta | Y | 10–1 | deci | d |
| 1021 | zetta | Z | 10–2 | centi | c |
| 1018 | exa | E | 10–3 | milli | m |
| 1015 | peta | P | 10–6 | micro | m |
| 1012 | tera | T | 10–9 | nano | n |
| 109 | giga | G | 10–12 | pico | p |
| 106 | mega | M | 10–15 | femto | f |
| 103 | kilo | k | 10–18 | atto | a |
| 102 | hecto | h | 10–21 | zeto | z |
| 101 | deca | da | 10–24 | yocto | y |