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1.2 SI units

Syllabus
9702–2028–2029
Topic
1.2
Level
AS

Learning objectives

1.2.1The following SI base quantities and their units: mass (kg), length (m)• recall the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K)1.2.2Derived units as products or quotients of the SI base units and use the• express derived units as products or quotients of the SI base units and use the derived units for quantities listed in this syllabus as appropriate1.2.3SI base units to check the homogeneity of physical equations• use SI base units to check the homogeneity of physical equations1.2.4The following prefixes and their symbols to indicate decimal submultiples or• recall and use the following prefixes and their symbols to indicate decimal submultiples or multiples of both base and derived units: pico (p), nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T)

The five required SI base quantities have fixed unit names and symbols

An SI base quantity is defined independently rather than from other quantities. For this syllabus, recall exactly these five mappings:

Base quantity SI base unit Symbol
mass kilogram kg
length metre m
time second s
electric current ampere A
thermodynamic temperature kelvin K

Use kilogram, not gram, as the base unit of mass; kelvin, not degree Celsius, for temperature; and ampere, not coulomb, for current. Unit symbols are case-sensitive.

Derive a unit by applying the quantity's defining relationship

A derived unit is a product or quotient of base units. Start from the equation that defines the quantity, replace each quantity by its SI unit, then simplify the powers.

F=ma⇒1 N=1 kg m s−2F=ma \quad\Rightarrow\quad 1\,\mathrm{N}=1\,\mathrm{kg\,m\,s^{-2}}

Pressure is force per area, p = F/A. Therefore Pa = N m⁻² = (kg m s⁻²)m⁻² = kg m⁻¹ s⁻². The final expression contains only SI base units.

A named unit such as N, J or Pa is not dimensionless. Replace it through a defining equation before cancelling factors or comparing units.

Check homogeneity by reducing every term to SI base units

A physical equation is homogeneous when every term that is added or subtracted has the same SI base units, and the units on the left-hand side match those on the right-hand side.

  1. Write the SI base units of each quantity.
  2. Include powers and products exactly as they appear.
  3. Simplify each term separately.
  4. Compare all additive terms and both sides.

For s = ut + ½at²: s has unit m; ut has (m s⁻¹)(s) = m; and at² has (m s⁻²)(s²) = m. Every term has unit m, so the equation is homogeneous.

Homogeneity is necessary but not sufficient. It cannot detect a wrong dimensionless number such as 2 instead of ½, so a homogeneous equation may still use the wrong physics.

SI prefixes rescale units by exact powers of ten

A prefix multiplies a base or derived unit by an exact power of ten. Prefix symbols are case-sensitive.

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

For length, 5.0 μm = 5.0 × 10⁻⁶ m. For area, the factor is squared: 3.0 mm² = 3.0(10⁻³ m)² = 3.0 × 10⁻⁶ m².

Do not change the case of a symbol: m means milli but M means mega. When a unit is squared or cubed, raise the prefix factor to the same power.