Physical Quantities, SI Units, and Prefixes
Fundamental and derived physical quantities, the 7 SI base units, supplementary and derived units, standard decimal prefixes (femto to giga), scientific notation, and unit conversions.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Identify the 7 SI base quantities, their base units, and standard symbols.
- Express derived units systematically in terms of SI base units.
- Apply standard SI decimal prefixes and convert non-standard laboratory units into coherent SI units.
Core Theory & Concepts
A physical quantity is any property of a phenomenon, body, or substance that can be quantified by measurement. The International System of Units (SI) defines 7 independent base quantities from which all other derived mechanical, electrical, thermal, and optical units are coherently generated.
The 7 SI Base Units
Length (metre, m), Mass (kilogram, kg), Time (second, s), Electric current (ampere, A), Thermodynamic temperature (kelvin, K), Amount of substance (mole, mol), and Luminous intensity (candela, cd).
Derived Units in Base Units
Force: Newton (N = kg m s⁻²); Work/Energy: Joule (J = N m = kg m² s⁻²); Power: Watt (W = J s⁻¹ = kg m² s⁻³); Pressure: Pascal (Pa = N m⁻² = kg m⁻¹ s⁻²); Potential Difference: Volt (V = J C⁻¹ = kg m² s⁻³ A⁻¹).
Density Conversion Factor
Since 1 g = 10⁻³ kg and 1 cm³ = 10⁻⁶ m³, 1 g cm⁻³ = (10⁻³ kg) / (10⁻⁶ m³) = 10³ kg m⁻³ = 1000 kg m⁻³. To convert g cm⁻³ to kg m⁻³, multiply by 1000.
Standard Metric Prefixes
femto (10⁻¹⁵), pico (10⁻¹²), nano (10⁻⁹), micro (10⁻⁶), milli (10⁻³), centi (10⁻²), deci (10⁻¹), kilo (10³), mega (10⁶), giga (10⁹), tera (10¹²).
2019 SI Redefinition Constants
Since May 2019, all 7 SI base units are defined by fixing exact numerical values of 7 defining physical constants: Planck constant h = 6.62607015 × 10⁻³⁴ J s (defines kg), Elementary charge e = 1.602176634 × 10⁻¹⁹ C (defines A), Boltzmann constant k = 1.380649 × 10⁻²³ J K⁻¹ (defines K), Avogadro constant N_A = 6.02214076 × 10²³ mol⁻¹ (defines mol), Speed of light c = 299792458 m s⁻¹ (defines m), Caesium transition frequency Δν_Cs = 9192631770 Hz (defines s), and Luminous efficacy K_cd = 683 lm W⁻¹ (defines cd). Physical artefacts (like the Le Grand K cylinder) are obsolete.
Scientific Notation & Significant Figures
Scientific notation represents any quantity as A × 10ⁿ where 1 ≤ A < 10 and n is an integer. Significant figures (sig figs) express experimental precision: 1. All non-zero digits are significant. 2. Zeros between non-zeros are significant (305 has 3). 3. Leading zeros are never significant (0.0042 has 2). 4. Trailing zeros after a decimal point are significant (4.500 has 4). When multiplying/dividing, round the final answer to the least number of sig figs among the inputs.
Common Misconceptions
To convert density from g cm⁻³ to kg m⁻³, one should divide by 1000.
Syllabus Topic Outline
- 1Fundamental vs derived physical quantities
- 2The 7 SI base units (kg, m, s, A, K, mol, cd)
- 3Expressing derived units in SI base units (J, N, Pa, V, W)
- 4Metric decimal prefixes (femto, pico, nano, micro, milli, centi, kilo, mega, giga)
- 5Unit conversions (density g cm⁻³ to kg m⁻³, speed km h⁻¹ to m s⁻¹)