SI Units and Prefixes

The Systeme International (SI) provides a coherent set of seven base units from which every derived unit in physics is built. NEET problems often test recognition of derived units (like the joule, newton or pascal) and the multiplying factor associated with SI prefixes such as nano, micro, milli, kilo, mega and giga.

Concept

The seven SI base quantities are length (metre, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), temperature (kelvin, K), amount of substance (mole, mol) and luminous intensity (candela, cd). All other units are derived from these. For example, force is $kg \cdot m \cdot s^{-2}$, named the newton (N). Energy is $kg \cdot m^2 \cdot s^{-2}$, named the joule (J). Pressure is $N/m^2$, named the pascal (Pa).

Prefixes denote powers of ten that scale a unit. Each prefix is a multiplicative factor attached to the unit symbol.

Formula Derivation

A general physical quantity $Q$ expressed with an SI prefix can be written as

$Q = n \times 10^{p} \cdot U$

where $n$ is the numerical value, $10^{p}$ is the prefix factor and $U$ is the base unit. Standard prefixes:

$\text{nano}=10^{-9},\;\text{micro}=10^{-6},\;\text{milli}=10^{-3},\;\text{centi}=10^{-2}$

$\text{kilo}=10^{3},\;\text{mega}=10^{6},\;\text{giga}=10^{9},\;\text{tera}=10^{12}$

For derived units, dimensional building blocks combine:

$[\text{Force}]=[M][L][T]^{-2},\quad [\text{Energy}]=[M][L]^{2}[T]^{-2}$

NEET-style Worked Example

Convert $5\ \mu A$ into ampere and then into nanoampere.

Step 1: Use the prefix $\mu = 10^{-6}$.

$5\ \mu A = 5 \times 10^{-6}\ A$

Step 2: Convert to nano ($10^{-9}$):

$5 \times 10^{-6}\ A = 5 \times 10^{-6} \times 10^{9}\ nA = 5 \times 10^{3}\ nA = 5000\ nA$

So $5\ \mu A = 5000\ nA$.

Common Confusions

• Kilogram is the base unit, not gram. This is the only base unit with a prefix in its name.
• Capital M vs small m. $M$ is mega ($10^{6}$); $m$ is milli ($10^{-3}$).
• Newton and joule are derived, not base. Watch for questions asking which are base SI units.
• Candela and mole are easy to forget but are base units.

Key Takeaways

• Memorise the seven SI base quantities and their units.
• Prefixes are pure powers of ten that multiply the unit.
• Derived units can always be reduced to base units using dimensions.
• $1\ kJ = 10^{3}\ J$, $1\ MW = 10^{6}\ W$, $1\ nm = 10^{-9}\ m$.