Measured quantity: Q = numerical value × unitExample: L = 1.2 × 1 m = 1.2 m.
Length: 1 km = 1,000 m1 m = 100 cm = 1,000 mm.
Mass: 1 kg = 1,000 gKilogram is the SI base unit of mass.
Volume: 1 L = 1,000 mL1 mL = 1 cm³; 1 L = 10⁻³ m³. Litre is accepted for use with SI.
Percentage uncertainty: (Δx / |x|) × 100%For a nonzero measured value x and absolute uncertainty Δx.
Derived force unit: 1 N = 1 kg m s⁻²Derived units combine base units.

Practice Questions

Quick CheckFive questions with feedback Worked ExamplesFollow the conversion factors Exam-Style QuestionsUnits problems and solutions Observation ChallengeClassify four observations

Observation

Words or numbers?

Physics starts by noticing. Some observations describe a quality; others measure a quantity.

Qualitative

Describe it

Uses words, qualities, or the senses. A number is not required.

roughsweetdark

Quantitative

Measure it

Uses numbers. Measured physical quantities usually include a unit; counts and dimensionless ratios are also quantitative.

9 cm1.5 kg8 °C

Quick check · 1/4

“The metal feels cold.”

What kind of observation is this?

Choose an answer to reveal the explanation.

A shared language

Meet the SI system

Scientists use one agreed system so a measurement means the same thing in every classroom, laboratory, and country.

How far?

Length

metre

Measured with a ruler.

Three more base units complete the set of seven:

Electric currentampereA
Amount of substancemolemol
Luminous intensitycandelacd

Combine base units to describe more:

speedm/s

volumem³

forceN

Scale up · scale down

A ladder of prefixes

Prefixes keep very large and very small measurements easy to read. Explore seven common scales from milli to kilo. The centre means no prefix; the full SI system includes additional prefixes.

Prefix

no prefix—10⁰

Move through the metric scale

× 11 m = 1 m

How good is the number?

Every measurement carries a doubt

Stating that doubt is part of the measurement, not an apology for it.

Readings spread

Random error

Repeated readings scatter around a mean, which may also be biased. Examples include judging a pendulum or reading a needle that will not settle.

Reduce its effect: repeat and average. This does not remove systematic bias.

Readings shift together

Systematic error

Every reading moves the same way, perhaps because a balance is mis-zeroed or a scale is viewed from an angle.

Improve it: find and remove the cause.

Repeatability

Precise

Repeated values cluster closely, even when they are all wrong.

Truth

Accurate

Values lie close to the accepted or true value.

Further study · formal uncertainty propagation and resistivity (optional for IGCSE)

Begin with fractions, percentages and powers. Use the course guidance here to identify reviewed relationships and remaining practical requirements. Suitability for other courses and shared resources requires a separate review.

Report the measurementL = 0.482 ± 0.002 mvalue ± absolute uncertainty

Convert it to a percentage(0.002 ÷ 0.482) × 100 = 0.4%absolute uncertainty ÷ |value| × 100 (value ≠ 0)

The following are conservative, first-order classroom estimates for small uncertainties. For independent standard uncertainties, statistical combination uses quadrature instead. Follow the convention specified in your course or experiment.

Adding or subtractingΔQ = ΔA + ΔB

Add the absolute uncertainties.

mm + mm

Multiplying or dividing%ΔQ = %ΔA + %ΔB

Add the percentage uncertainties.

% + %

Raising to a power n%ΔQ = |n| × %ΔA

Multiply the percentage uncertainty by the absolute value of the power.

n × %

Exam diagrams for this topic1 figure to inspect and practiseQuestions, hints and marking points in one compact subsection.

See it. Read it. Work it.

These figures come from GioPhysics practice papers. Open one, decode the drawing, work the guided questions, then follow its link to the full paper question.

01
InspectRead the figure comment.
02
TraceFollow labels, arrows and axes.
03
AnswerWork one part at a time.
04
CheckReveal hints and marking points.

IGCSE

01Fig. 10.1Physical quantities and measurement techniques · DensityIGCSE

Figure comment

Fig. 10.1Two measuring cylinders drawn side by side, each with graduations up the wall and a curved meniscus. The first holds water alone, its surface at the 50.0 cm³ mark. The second holds the same water with the stone lowered in on a thread that runs up and out of the cylinder; the stone lies fully submerged near the base and the surface now stands at the 68.0 cm³ mark.

Read the comment once, then trace every arrow, label, axis or component in the drawing before opening the questions.

1.1 Physical quantities and measurement techniques 1.4 Density Open IGCSE question · Motion, forces and energy Q10

Guided questions 5 parts

Reading cue. The 50.0 cm³ is water alone and the 68.0 cm³ is water with the stone in, so the quantity everything turns on is the difference between the two levels, and it is printed on neither scale.

aDetermine Determine the volume of the stone from the two readings in Fig. 10.1.
recall2 marks
Check answer 2 marks
1. volume = 68.0 - 50.0 (1)
2. = 18.0 cm³ (1)
bDetermine A second stone, identical to the first, is lowered into the same cylinder on a thread beside it. Determine the new reading of the water surface, and state one condition that must hold for your answer to be correct.
routine3 marks
Check answer 3 marks
1. the second stone displaces a further 18.0 cm³ (1)
2. new reading = 68.0 + 18.0 = 86.0 cm³ (1)
3. condition: both stones must be completely below the surface, and the water must not reach the top of the cylinder (1)
cExplain The cylinder in Fig. 10.1 is graduated in divisions of 1 cm³, so each of the two levels can be judged only to within half a division. Explain why the volume of the stone is known far less precisely than either reading, supporting your answer with figures.
demanding3 marks
Check answer 3 marks
1. each reading may be out by up to 0.5 cm³, so their difference may be out by up to 1 cm³ (1)
2. 1 cm³ in 18.0 cm³ is about 6% (1)
3. 0.5 cm³ in 68.0 cm³ is less than 1%, so subtracting two large readings to obtain a small difference magnifies the error (1)
dSuggest A larger stone is to be measured, but lowering it into the cylinder drawn in Fig. 10.1 would take the water above the top graduation. Suggest a change to the method that still uses the same cylinder, and explain why the volume obtained is still correct.
top of the paper3 marks
Check answer 3 marks
1. pour out some water first, so that the starting level is much lower, for example 20 cm³ rather than 50.0 cm³ (1)
2. enough water must remain to cover the stone completely once it is lowered in (1)
3. only the difference between the two readings is used, and that difference does not depend on the starting level (1)

Transfer challenge

A metal statue is far too large for any measuring cylinder. It is lowered on a thread into an overflow can that has been filled until water just stops running from the spout, and the water pushed out is collected in a measuring cylinder, which then reads 240 cm³. Determine the volume of the statue, and explain why the can must be left to stop dripping before the statue is lowered in.

Check answer 4 marks

volume of statue = 240 cm³ (1)
the water pushed out has the same volume as the part of the statue below the surface, so the statue must be fully submerged (1)
if the can is still over-full, water standing above the level of the spout runs out on its own (1)
that extra water would be collected as well and the volume obtained would be too large (1)

Worked Examples

Convert a measured length

A cable is 1,543 mm long. Express its length in metres.

Use 1 m = 1,000 mm.
1,543 mm × (1 m / 1,000 mm) = 1.543 m.
Check: the metre is larger, so the numerical value is smaller.

Convert a volume into cubic metres

A beaker contains 250 mL.

250 mL ÷ 1,000 = 0.250 L.
1 L = 10⁻³ m³, so 0.250 × 10⁻³ = 2.50 × 10⁻⁴ m³.
Also, 1 mL = 1 cm³, so the volume is 250 cm³.

For cubed units, cube the length factor: 1 cm³ = (0.01 m)³ = 10⁻⁶ m³.

Downloads & Resources

Summary NotesCore units lesson · PDF Classroom Slides22 slides · PPTX PresentationOpen in browser WorksheetsPDF with solutions

The extended uncertainty section is available on this page.

Try a Game

Vector Run

Continue exploring motion in the chapter’s interactive game.

Play now →

Cambridge 9702 · focused teaching and practice

Complete the objective

Open a topic for its explanation, worked example and original practice. The AS and additional A-Level requirements remain separate. Practical preparation does not replace supervised laboratory work.

AS · 1.1.2

Estimate, calculate, then sanity-check

Teaching, example & practice

General browsing: select Cambridge AS or A2 and your examination year for a recommended route.

An estimate is a defensible approximate value, not a random guess. Start with a familiar benchmark, state a simple model, round the input values to one significant figure, calculate with units, and check whether the result is plausible.

Useful starting points are a person's height around 2 m, walking speed around 1 m s⁻¹, a book's mass around 0.5 kg, room temperature around 300 K, water density around 10³ kg m⁻³, and gravitational field strength around 10 N kg⁻¹. These are rough benchmarks, not precise constants or universal human measurements.

Build an unfamiliar quantity from familiar ones: force from mg, pressure from F/A, energy from Fs, power from E/t and current from P/V. Give a range if uncertain geometry dominates. An estimate should not acquire unjustified decimal places.

Worked example

Estimate the extra energy needed to carry a 10 kg bag up one 3 m storey, and the average useful power if it takes 10 s.

Model the bag's weight as 10 × 10 = 100 N.
The vertical work is about 100 × 3 = 300 J.
Average useful power is about 300/10 = 30 W; this excludes lifting the person and metabolic losses.

About 3 × 10² J and 3 × 10¹ W.

Try the original practice · 6 marks →Objective and coverage record

Scope and sources

Original GioPhysics teaching and practice, checked against the syllabus. This section does not certify unrelated videos, downloads or the rest of a shared lesson.

Cambridge syllabus · printed page 16 — Required objective scope verified; explanations and assessment below are original.
Cambridge syllabus · printed page 16 — Same AS demand checked in the local official syllabus PDF.

AS · 1.2.2 / 1.2.3

Construct units and test an equation

Teaching, example & practice

General browsing: select Cambridge AS or A2 and your examination year for a recommended route.

Write the defining equation, replace each quantity with its unit, cancel units algebraically, and collect powers of kg, m, s, A and K. A named unit can always be expanded; a quantity divided by another of the same kind is dimensionless.

For an equation to be homogeneous, every added or subtracted term must have the same units and both sides must agree. Numerical constants such as 2 and π do not change units. Matching units is necessary, not sufficient: it cannot distinguish v² = u² + as from v² = u² + 2as.

Quantity	Definition used	SI base-unit form
density	m/V	kg m⁻³
force	ma	kg m s⁻²
pressure; stress; Young modulus	F/A; stress/strain	kg m⁻¹ s⁻²
moment; energy	force × distance	kg m² s⁻²
power	energy/time	kg m² s⁻³
charge	It	A s
potential difference	energy/charge	kg m² s⁻³ A⁻¹
resistance	V/I	kg m² s⁻³ A⁻²
resistivity	RA/L	kg m³ s⁻³ A⁻²
spring constant	force/extension	kg s⁻²
intensity	power/area	kg s⁻³
frequency; strain	1/time; extension/length	s⁻¹; dimensionless

Worked example

A model for resistive force is F = bv². Find the base units of b and check whether F = bv is homogeneous with that same b.

[b] = [F]/[v]² = (kg m s⁻²)/(m² s⁻²) = kg m⁻¹.
Then [bv] = kg s⁻¹, unlike force kg m s⁻².
The linear model needs a different coefficient, of unit kg s⁻¹.

b has unit kg m⁻¹; F = bv with that coefficient is not homogeneous.

Try the original practice · 6 marks →Objective and coverage record

Scope and sources

Original GioPhysics teaching and practice, checked against the syllabus. This section does not certify unrelated videos, downloads or the rest of a shared lesson.

Cambridge syllabus · printed page 16 — Required objective scope verified; explanations and assessment below are original.
Cambridge syllabus · printed page 16 — Same AS demand checked in the local official syllabus PDF.

AS · 1.2.4

All ten AS prefixes, including compound units

Teaching, example & practice

General browsing: select Cambridge AS or A2 and your examination year for a recommended route.

Replace the prefix with its power of ten before calculating. Prefix symbols are case-sensitive: m means milli while M means mega. For an area or volume, raise the entire prefixed length unit to the power: mm² means (10⁻³ m)², not 10⁻³ m².

A prefix on a named derived unit changes that whole unit: 1 MPa = 10⁶ Pa. For a quotient, convert numerator and denominator separately. The SI base mass unit remains kg; 1 mg = 10⁻⁶ kg.

Prefix	Symbol	Multiplier
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

Worked example

Convert 2.4 mm² and 3.0 kN mm⁻² to SI units.

2.4 mm² = 2.4 × (10⁻³ m)² = 2.4 × 10⁻⁶ m².
3.0 kN mm⁻² = 3.0 × 10³ N / 10⁻⁶ m² = 3.0 × 10⁹ Pa.

2.4 × 10⁻⁶ m² and 3.0 GPa.

Try the original practice · 9 marks →Objective and coverage record

Scope and sources

Original GioPhysics teaching and practice, checked against the syllabus. This section does not certify unrelated videos, downloads or the rest of a shared lesson.

Cambridge syllabus · printed page 16 — Required objective scope verified; explanations and assessment below are original.
Cambridge syllabus · printed page 16 — Same AS demand checked in the local official syllabus PDF.

Extra challenging questions

Take the ideas further with course-specific extension questions, supplied-data graphs and worked solutions.

Units & Measurement

Give every number meaning.

Lesson Overview

Learning Objectives

Key Concepts

Same amount, new unit

Key Formulae

Practice Questions

Words or numbers?

Describe it

Measure it

“The metal feels cold.”

Meet the SI system

metre

A ladder of prefixes

Every measurement carries a doubt

Random error

Systematic error

Precise

Accurate

See it. Read it. Work it.

IGCSE

Worked Examples

Quick Quiz

Downloads & Resources

Related Content

Try a Game

Complete the objective

Estimate, calculate, then sanity-check

Worked example

Construct units and test an equation

Worked example

All ten AS prefixes, including compound units

Worked example

Extra challenging questions