Si units

The SI system defines six base quantities used in this syllabus:

• Mass (kg)
• Length (m)
• Time (s)
• Electric current (A)
• Thermodynamic temperature (K)
• Amount of substance (mol)

Every other physical quantity has a derived unit built from these base quantities through multiplication or division.

Force, energy, power, pressure, charge, potential difference, resistance, and frequency all reduce to combinations of kg, m, s, and A.

Key Definition A physical equation is homogeneous when every term on both sides of the equation has the same base units.

Homogeneity is a necessary but not sufficient condition for correctness: it cannot detect missing dimensionless constants, such as ½ or 2π.

Prefixes attach to any base or derived unit to indicate decimal multiples or submultiples, ranging from pico (10⁻¹²) to tera (10¹²):

• tera (T) = 10¹²
• giga (G) = 10⁹
• mega (M) = 10⁶
• kilo (k) = 10³
• deci (d) = 10⁻¹
• centi (c) = 10⁻²
• milli (m) = 10⁻³
• micro (μ) = 10⁻⁶
• nano (n) = 10⁻⁹
• pico (p) = 10⁻¹²

The unifying idea is that the SI base units provide a complete and consistent framework for measurement.

Derived units, prefixes, and homogeneity testing are all built from this base.

In examinations, candidates must:

• Express derived units in terms of the SI base units
• Perform homogeneity checks correctly
• Convert prefixed values to standard SI form before substitution

Common pitfalls include:

• Writing N or J as if they were base units
• Mistaking the kilogram for a derived unit
• Confusing the symbols M (mega) and m (milli or metre)
• Assuming that homogeneity proves physical correctness