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Unit 1 · Lesson 1 of 3 10 min

Physical Quantities and SI Units

A number on its own is gossip. A number with a unit is physics.

A nurse in a Kano clinic writes three things on a chart: 37.2, 120/80, 65. Hand that chart to a stranger and it is nonsense. Write 37.2 °C, 120/80 mmHg, 65 kg, and suddenly anyone in the world can read the patient's temperature, blood pressure and mass. That tiny tail after each number, the unit, is where physics begins.

Physical Quantities

A physical quantity is any property of a body or a phenomenon that can be measured: length, mass, time, temperature, speed, force, pressure. Every physical quantity is written as

quantity=number×unit,\text{quantity} = \text{number} \times \text{unit},

so "65 kg" means 65 lots of the standard kilogram. Change the unit and the number changes with it: the same patient is 65 000 g. The quantity itself has not changed at all.

Scientists agreed on one shared system, the SI (Système International d'Unités). It starts from seven fundamental (base) quantities, which are independent of each other and cannot be defined in terms of other quantities. Every other quantity is a derived quantity, obtained by multiplying or dividing fundamental quantities.

The seven SI base quantities
Base quantitySI unitSymbol
Lengthmetrem
Masskilogramkg
Timeseconds
Electric currentampereA
Thermodynamic temperaturekelvinK
Amount of substancemolemol
Luminous intensitycandelacd

Worked example

Worked example: Expressing a derived unit in base units

Express the unit of pressure, the pascal (Pa), in SI base units.

  1. 1
    Start from the definition

    Pressure =forcearea= \dfrac{\text{force}}{\text{area}}, so 1 Pa=1 N m−21\,\text{Pa} = 1\,\text{N m}^{-2}.

SI Prefixes

A red blood cell is about 0.00000750.0000075 m across; Abuja to Lagos by air is roughly 500 000500\,000 m. Writing all those zeros invites mistakes, so we use standard form (7.5×10−67.5 \times 10^{-6} m) and prefixes, which are just names for powers of ten.

picop10⁻¹²atom ~100 pm nanon10⁻⁹virus ~100 nm microμ10⁻⁶red cell ~7.5 μm millim10⁻³tablet 500 mg centic10⁻²fingernail ~1 cm 1base unit10⁰1 m, 1 kg, 1 s kilok10³patient 65 kg megaM10⁶power plant, MW gigaG10⁹data, GB Each prefix is a power of ten
SI prefixes. The prefixes you must know. Moving one circle to the right multiplies by 10310^3 (except around centi). The examples are rough sizes, for feel.

Worked example

Worked example: Conversion of units using prefixes

Replace the prefix by its power of ten, then tidy into standard form.

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    A tablet of 450 mg in kilograms

    450 mg=450×10−3 g=0.450 g=0.450×10−3 kg=4.5×10−4 kg450\,\text{mg} = 450 \times 10^{-3}\,\text{g} = 0.450\,\text{g} = 0.450 \times 10^{-3}\,\text{kg} = 4.5 \times 10^{-4}\,\text{kg}.

Quick check

Did it land?

1. Which of these is a fundamental (base) SI quantity?
2. The pascal, the SI unit of pressure, expressed in SI base units is…

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