Master A-Level Physics: SI Units, Prefixes, and Estimation Techniques

Physics studies the world through measurement. A physical quantity is anything that can be measured, and every quantity must have two things: a numerical value and a unit. Examples of physical quantities include energy, power, density, area, momentum, time, weight, mass, resistance, and angle.

Types of Quantities

There are two broad categories of quantities: base quantities and derived quantities. In this overview the focus is on the seven base quantities and their corresponding SI units, because they form the foundation for all derived quantities.

SI Base Quantities and Units

The seven SI base quantities that must be memorised are:

• Length – metre (m)
• Mass – kilogram (kg)
• Time – second (s)
• Electric current – ampere (A), named after André‑Marie Ampère
• Temperature – kelvin (K), named after Lord Kelvin
• Amount of substance – mole (mol)
• Luminous intensity – candela (cd)

Remembering the symbols and units for these base quantities is essential for any A‑level physics student.

Estimation Example: Kinetic Energy of a Sprinter

A common practice problem asks for an approximate kinetic energy of an Olympic athlete running at maximum speed in a 100 m race. Using the kinetic‑energy formula

[ KE = \frac12 mv^2 ]

we can make reasonable approximations:

• Velocity (v) – Usain Bolt’s world‑record time of about 10 s for 100 m gives a speed of roughly 10 m s⁻¹.
• Mass (m) – An average sprinter’s mass can be taken as about 80 kg.

Plugging these numbers in:

[ KE = \frac12 \times 80\ \text{kg} \times (10\ \text{m s}^{-1})^2 \approx 4000\ \text{J} ]

Thus the kinetic energy is on the order of a few kilojoules, illustrating how order‑of‑magnitude estimation works in practice.

SI Prefixes

Prefixes allow us to write very large or very small numbers compactly. The most common prefixes and their factors are:

• Tera (T) – 10¹²
• Giga (G) – 10⁹ (e.g., gigabytes)
• Mega (M) – 10⁶
• Kilo (k) – 10³ (e.g., kilograms, kilometres)
• Deci (d) – 10⁻¹
• Centi (c) – 10⁻² (e.g., centimetres)
• Milli (m) – 10⁻³ (e.g., millimetres)
• Micro (µ) – 10⁻⁶
• Nano (n) – 10⁻⁹
• Pico (p) – 10⁻¹²

“The prefixes are helpful in helping you to estimate values,” because they immediately signal the size of a number and help check whether an answer is plausible.

Writing Physical Quantities

A physical quantity is written as a symbol, a numerical value, and a unit. For example, the length of a phone might be recorded as 12.3 cm. The prefix c (centi) corresponds to a factor of 10⁻², so the same length expressed in metres is

[ 12.3 \times 10^{-2}\ \text{m} ]

Understanding how to convert between prefixes and the base SI unit is a key skill.

Calculator Shortcut for Conversions

Most scientific calculators have an “ENG” (engineering) button that displays numbers in engineering notation, i.e., powers of ten that are multiples of three. Pressing ENG (or SHIFT ENG) lets you quickly switch between prefixes such as nano, pico, and femto, making it easy to read and rewrite values without manual exponent arithmetic.

Order of Magnitude Estimation Practice

Practising order‑of‑magnitude estimates sharpens intuition. Some example checks:

• Mass of a coin – roughly 10⁻⁴ kg (0.1 g).
• Thickness of a sheet of paper – not 10⁻² m (1 cm); paper is much thinner, so the estimate is incorrect.
• Weight of an apple – about 1 N (≈100 g mass), which is reasonable.
• Human body temperature – 10 K is far too low; normal body temperature is around 310 K.

The general approach is to compare the quantity with familiar objects, use known prefixes, and verify that the resulting exponent makes sense.

Conclusion and Next Steps

Knowing the SI base units, mastering prefixes, and practising estimation are foundational for physics. The next topics will build on this groundwork, covering uncertainties, scalars, and vectors.