Physical Quantities, Units & Estimates

Objectives

Lesson outcomes

Use physical quantities as a numerical value paired with a unit and make sensible order-of-magnitude estimates.
Recall SI base quantities and units and express derived units in base-unit form.
Use prefixes confidently and check whether equations are dimensionally consistent.

Syllabus

CIE 9702 syllabus points

6 linked

1.1.1 understand that all physical quantities consist of a numerical magnitude and a unit
1.1.2 make reasonable estimates of physical quantities included within the syllabus
1.2.1 recall the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K)
1.2.2 express derived units as products or quotients of the SI base units and use the derived units for quantities listed in this syllabus as appropriate
1.2.3 use SI base units to check the homogeneity of physical equations
1.2.4 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)

Lesson Notes

Student guidance and lesson notes

Overview

This lesson sets up the language of almost every calculation in the course. The goal is to become quick and accurate with units, prefixes, and estimates so that later physics does not get slowed down by avoidable mistakes.

What You Need to Know

Every physical quantity has a numerical magnitude and a unit.
You should know the core SI base quantities used in the syllabus and their units.
Derived units should be understood as combinations of SI base units rather than just labels to memorise.
Prefixes such as milli, micro, kilo, and mega need to be handled fluently in both directions.
Order-of-magnitude estimates are useful because they help you judge whether an answer is sensible.
Checking the homogeneity of an equation is a useful way to spot mistakes in units or structure.

How to Work Through It

Start by revising the difference between a quantity, its value, and its unit.
Work through the SI base units and derive several compound units from them.
Practise converting with prefixes until the scale changes feel automatic.
Finish with estimation and homogeneity checks so the topic stays practical rather than purely definitional.

Check Your Understanding

Can you state the SI unit of a named quantity without hesitation?
Can you rewrite a derived unit in base-unit form?
Does your estimate have the right scale even before you calculate precisely?
Can you explain why an equation is or is not homogeneous?

Common Mistakes

Treating prefixes as decoration instead of powers of ten.
Using a quantity name and a unit as if they were interchangeable.
Memorising derived units without understanding how they are built.
Ignoring an absurd estimate because the calculation process looked correct.

Next Steps

Keep a short personal list of prefixes and awkward derived units until they become automatic.
Carry this unit discipline into the next lesson on uncertainty, where precise reporting matters even more.