Measuring physical quantities accurately and checking equations
Physics rests on measurement. The SI system has seven base units: metre, kilogram, second, ampere, kelvin, mole and candela. All other units, such as the newton (kg m s⁻²) and joule (kg m² s⁻²), are derived from them. Each physical quantity has dimensions written in terms of mass [M], length [L] and time [T]; for example, force has dimensions [MLT⁻²].
Dimensional analysis uses the principle of homogeneity: every term in a valid equation must have the same dimensions. This lets you check formulas, convert units between systems and even derive relations, such as showing that a pendulum’s period depends on √(l/g). Every measurement has some uncertainty. Absolute error is the difference from the true value, and relative or percentage error compares it with the value measured. When quantities are multiplied or divided, their relative errors add. Significant figures show how precise a result is, and answers should not be quoted more precisely than the least precise data.
Why it matters
Accurate units and error analysis are essential in laboratories, medicine dosage, engineering and manufacturing, where a small mistake can be costly. Dimensional checks catch errors in formulas before calculations are done. Scientists worldwide can share results only because they use the same SI units. These skills apply to every numerical topic in physics and chemistry.
Key terms
- Base unit
- One of the seven fundamental SI units from which all other units are derived.
- Dimensional formula
- An expression showing how a quantity depends on mass, length, time and other base quantities.
- Significant figures
- The digits in a measurement that are known reliably plus the first uncertain digit.
- Relative error
- The ratio of the absolute error to the measured value of a quantity.