What are the basic units of measurement in the Cambridge Lower Secondary Mathematics curriculum?

In the Cambridge Lower Secondary Mathematics curriculum, the basic units of measurement include meters for length, kilograms for mass, and seconds for time. These are part of the International System of Units (SI), which is widely used in scientific and educational contexts.

How do you convert between different units of measurement?

To convert between different units of measurement, you need to multiply or divide by conversion factors. For example, to convert meters to centimeters, multiply by 100, since there are 100 centimeters in a meter. Understanding conversion factors is essential in the Geometry and Measure section of the Cambridge Lower Secondary Mathematics curriculum.

Why is it important to understand units of measurement in Geometry and Measure?

Understanding units of measurement is crucial in Geometry and Measure because it allows students to accurately calculate dimensions, areas, and volumes. This knowledge is fundamental for solving real-world problems and is a key component of the Cambridge Lower Secondary Mathematics curriculum.

What is the difference between metric and imperial units of measurement?

Metric units, such as meters and kilograms, are part of the International System of Units (SI) and are based on powers of ten, making them easy to convert. Imperial units, such as feet and pounds, are used mainly in the United States and are not as straightforward to convert. The Cambridge Lower Secondary curriculum primarily focuses on metric units.

How can understanding units of measurement help in everyday life?

Understanding units of measurement helps in everyday life by enabling accurate measurement and comparison of quantities, such as cooking ingredients, distances, and weights. This practical application of Geometry and Measure is emphasized in the Cambridge Lower Secondary Mathematics curriculum to prepare students for real-world scenarios.

Why is "Using the linear conversion factor instead of squaring it when converting area." a common mistake in Units of Measurements?

Why it happens: Students remember that 1 m = 100 cm and apply × 100 to areas as well. How to avoid it: Always square the linear factor for area: 1 m^2 = 100^2 = 10,000 cm^2.

Why is "Multiplying by $100$ or $10{,}000$ when converting volume from $\text{m}^3$ to $\text{cm}^3$." a common mistake in Units of Measurements?

Why it happens: Students forget that volume needs the linear factor **cubed**. How to avoid it: Cube the linear factor for volume: 1 m^3 = 100^3 = 1,000,000 cm^3.

Why is "Using time in minutes with a speed in $\text{km/h}$ without converting." a common mistake in Units of Measurements?

Why it happens: It is tempting to substitute the numbers straight into the formula and ignore the units. How to avoid it: Make every quantity match the units of the answer. Convert 30 minutes to 0.5 hours before dividing.

Why is "Reading $1.5$ hours as $1$ hour $50$ minutes." a common mistake in Units of Measurements?

Why it happens: Students treat the decimal part as if time used base 100 instead of base 60. How to avoid it: Multiply the decimal part by 60 to get minutes: 0.5 × 60 = 30, so 1.5 h = 1 h\,30 min.

Why is "Writing an answer without its unit." a common mistake in Units of Measurements?

Why it happens: Students focus on getting the number right and forget the unit at the end. How to avoid it: Every measurement answer should include the unit — 5 kg, 12 cm, 30 m/s — not just a bare number.

Geometry and MeasureCambridge Lower Secondary Mathematics (Checkpoint Exam Prep)

Units of Measurements

Work through the notes, try the practice questions, then take the quiz. The report tells you exactly what to revise next.

Previous Next

Learn this Topic

Start with the slides for the quick version, then go deeper with the full study notes.

Short Study Notes in the form of Slides

Read the notes first. If the method in a worked example clicks, you're ready for the questions.

Page 1 / 0

Detailed Notes

Clear explanations, examples and a recap to help you really understand this topic.

Take these study notes with you

Download a branded PDF — full prose, callouts, recap and memorise list for Units of Measurements, ready to print or save offline.

Units of Measurements — Cambridge Lower Secondary Maths, Checkpoint

Revise every unit you need for Checkpoint — metric lengths, masses and capacities, the trickier conversions for area and volume, compound units like speed and density, and working with time. Clear pictures and a steady method for every conversion.

At a glance

Metric units use powers of 10: kilo = 1000, centi = 1/100, milli = 1/1000.
Length: $1\text{ km} = 1000\text{ m}$ ; $1\text{ m} = 100\text{ cm}$ ; $1\text{ cm} = 10\text{ mm}$ .
Mass: $1\text{ kg} = 1000\text{ g}$ ; $1\text{ g} = 1000\text{ mg}$ ; $1\text{ tonne} = 1000\text{ kg}$ .
Capacity: $1\text{ L} = 1000\text{ mL}$ ; $1\text{ mL} = 1\text{ cm}^3$ .
Area conversions square the linear factor: $1\text{ m}^2 = 10{,}000\text{ cm}^2$ .
Volume conversions cube the linear factor: $1\text{ m}^3 = 1{,}000{,}000\text{ cm}^3$ .
Compound units link two quantities — speed is distance ÷ time; density is mass ÷ volume.
Time uses base 60 and 24: $60$ s in a minute, $60$ min in an hour, $24$ h in a day.

What you’ll learn

Mapped to the Cambridge Lower Secondary Mathematics curriculum framework.

Convert between metric units of length, mass and capacity using powers of 10.
Convert between metric units of area and volume by squaring and cubing the linear conversion factor.
Use compound units — speed, density and rates — including unit conversions.
Add, subtract and convert times using the 24-hour clock and base-60 arithmetic.

The metric system — powers of 10

Kilo, centi and milli are all powers of ten — multiply or divide by 10, 100 or 1000.

The metric system is built around powers of 10, which makes conversions much easier than working with old units like feet and gallons.

The prefixes you need are:

kilo- means $1000$ ,
centi- means $\frac{1}{100}$ (one hundredth),
milli- means $\frac{1}{1000}$ (one thousandth).

The same prefixes work for length, mass and capacity:

Length: $1\text{ km} = 1000\text{ m}$ , $1\text{ m} = 100\text{ cm}$ , $1\text{ cm} = 10\text{ mm}$ .
Mass: $1\text{ kg} = 1000\text{ g}$ , $1\text{ g} = 1000\text{ mg}$ , $1\text{ tonne} = 1000\text{ kg}$ .
Capacity: $1\text{ L} = 1000\text{ mL}$ , and importantly $1\text{ mL} = 1\text{ cm}^3$ .

Going down the ladder you multiply; going up you divide.

A simple method that never lets you down:

Write down what you have, with its unit.
Decide whether the new unit is larger or smaller.
Multiply when moving to a smaller unit (the number gets bigger), divide when moving to a larger unit.

For example, $2.5\text{ kg} = 2.5 \times 1000 = 2500\text{ g}$ , and $750\text{ mL} = 750 \div 1000 = 0.75\text{ L}$ .

kilo = 1000, centi = 1/100, milli = 1/1000.
Same prefixes for length, mass and capacity.
Smaller unit needs a bigger number — multiply.
Larger unit needs a smaller number — divide.

Area conversions — square the factor

Switching units of area squares the conversion factor — $1\text{ m}^2 = 10{,}000\text{ cm}^2$ .

Area conversions trip up a lot of students because the conversion factor between linear units gets squared when you switch to area units.

A square that is $1\text{ m}$ along each side has an area of $1\text{ m}^2$ . The same square is $100\text{ cm}$ along each side, so its area is $100 \times 100 = 10{,}000\text{ cm}^2$ .

100 × 100 = 10,000 — the linear factor is squared.

The same idea applies to every area conversion:

$1\text{ cm}^2 = 10 \times 10 = 100\text{ mm}^2$ .
$1\text{ km}^2 = 1000 \times 1000 = 1{,}000{,}000\text{ m}^2$ .

So $3.2\text{ m}^2 = 3.2 \times 10{,}000 = 32{,}000\text{ cm}^2$ , and $50{,}000\text{ cm}^2 = 50{,}000 \div 10{,}000 = 5\text{ m}^2$ .

A reliable check: when you convert to a smaller unit, the number gets bigger. Always glance at the answer to see if it feels right.

Square the linear factor when you change units of area.
$1\text{ m}^2 = 10{,}000\text{ cm}^2$ and $1\text{ cm}^2 = 100\text{ mm}^2$ .
Smaller unit → bigger number (and bigger unit → smaller number).
Use the same multiply/divide logic as linear conversions.

Volume conversions — cube the factor

Switching units of volume cubes the conversion factor — $1\text{ m}^3 = 1{,}000{,}000\text{ cm}^3$ .

Volume conversions take the same idea one step further: the linear conversion factor is cubed.

A cube that is $1\text{ m}$ along each edge has a volume of $1\text{ m}^3$ . In centimetres each edge is $100\text{ cm}$ , so the volume is $100 \times 100 \times 100 = 1{,}000{,}000\text{ cm}^3$ .

100 × 100 × 100 = 1,000,000 — the linear factor is cubed.

So:

$1\text{ cm}^3 = 10 \times 10 \times 10 = 1000\text{ mm}^3$ .
$1\text{ m}^3 = 1{,}000{,}000\text{ cm}^3$ .

A very useful link to remember: $1\text{ mL} = 1\text{ cm}^3$ , so $1\text{ L} = 1000\text{ cm}^3$ .

A tank with a volume of $0.25\text{ m}^3$ holds $0.25 \times 1{,}000{,}000 = 250{,}000\text{ cm}^3 = 250\text{ L}$ of water.

Cube the linear factor for volume conversions.
$1\text{ m}^3 = 1{,}000{,}000\text{ cm}^3$ and $1\text{ cm}^3 = 1000\text{ mm}^3$ .
$1\text{ mL} = 1\text{ cm}^3$ and $1\text{ L} = 1000\text{ cm}^3$ .
Use the same multiply/divide logic with the cubed factor.

Compound units — speed, density and rates

A compound unit combines two quantities — keep the units consistent.

Compound units combine two measurements into a single rate. The two you meet most often are speed and density.

Speed measures how fast something moves: $\text{speed} = \frac{\text{distance}}{\text{time}}.$

Common units: $\text{km/h}$ (kilometres per hour), $\text{m/s}$ (metres per second). A car at $60\text{ km/h}$ covers $60$ kilometres in $1$ hour.

Density measures how heavy a material is for its size: $\text{density} = \frac{\text{mass}}{\text{volume}}.$

A common unit is $\text{g/cm}^3$ . Water has a density of $1\text{ g/cm}^3$ ; iron is about $7.9\text{ g/cm}^3$ .

You can rearrange both formulae. For speed, $\text{distance} = \text{speed} \times \text{time}$ and $\text{time} = \dfrac{\text{distance}}{\text{speed}}$ .

Cover the unknown letter — what remains is the formula.

The most important habit: make the units match before you calculate. If a speed is given in $\text{km/h}$ but the time is in minutes, convert the time to hours (or the speed to $\text{km/min}$ ) first.

A train travels $180\text{ km}$ in $2.5$ hours, so its speed is $180 \div 2.5 = 72\text{ km/h}$ . To convert to $\text{m/s}$ : $72\text{ km/h} = 72 \times 1000 \div 3600 = 20\text{ m/s}$ .

Speed = distance ÷ time; density = mass ÷ volume.
Rearrange when needed — distance = speed × time.
Make the units consistent before you calculate.
To convert km/h to m/s, multiply by $1000$ and divide by $3600$ .

Working with time

Time uses base 60 and base 24 — and you need both the 12-hour and 24-hour clocks.

Time is the one place where everyday units do not use powers of 10. You need to remember:

$60$ seconds in a minute,
$60$ minutes in an hour,
$24$ hours in a day,
$7$ days in a week, $365$ (or $366$ ) days in a year.

The 12-hour clock uses am and pm (with $12$ noon and $12$ midnight). The 24-hour clock runs from $00\!:\!00$ to $23\!:\!59$ . So $3\!:\!45\text{ pm}$ is $15\!:\!45$ , and $7\!:\!30\text{ am}$ is $07\!:\!30$ .

Step up to the next whole hour, jump full hours, then add the minutes.

When you add or subtract time, never just subtract the numbers — they roll over at $60$ . A reliable method is to step up to the next whole hour, then jump full hours, then add the leftover minutes. From $09\!:\!50$ to $11\!:\!25$ : $10$ min + $1$ h + $25$ min = $1$ h $35$ min.

Working with decimal hours also catches people out. $1.5$ hours is $1$ h $30$ min, not $1$ h $50$ min. $2.25$ hours is $2$ h $15$ min. Multiply the decimal part by $60$ to turn it into minutes.

60 s in a min, 60 min in an hour, 24 h in a day.
12-hour clock uses am/pm; 24-hour clock goes 00:00 to 23:59.
Add time with a number line — never just subtract the digits.
Decimal hours: multiply the decimal part by 60 for minutes.

Choosing the right unit

Pick a unit that suits the size of the thing you are measuring.

Choosing a sensible unit makes your answers easier to read and to check.

A door is best measured in metres, not millimetres.
An ant's length sits in millimetres, not metres.
A box of cereal weighs in grams; a person in kilograms; a truckload in tonnes.
A small bottle of medicine is in millilitres; a bottle of water in litres.

When the numbers in your answer look very large or very small, ask yourself if a different unit would make it tidier. For example, $4{,}500\text{ m}$ is more naturally written as $4.5\text{ km}$ , and $0.0025\text{ kg}$ as $2.5\text{ g}$ .

In real questions the first job is often a quick conversion so that every quantity uses the same unit. A garden $6\text{ m}$ long and $200\text{ cm}$ wide has an area of $6 \times 2 = 12\text{ m}^2$ — but only after you turn $200\text{ cm}$ into $2\text{ m}$ . Forgetting that step is a common slip.

Match the unit to the size of the object.
Convert all quantities to the same unit before calculating.
Rewrite very large or very small numbers in a tidier unit.
$1\text{ tonne} = 1000\text{ kg}$ is useful for heavy objects.

Where you'll use this next

Conversions and compound units show up everywhere in science and beyond.

Comfort with units pays off in every science and almost every later maths topic:

Physics is built on compound units — speed, acceleration, force, density, pressure.
Chemistry uses concentrations (g/L, mol/L) and converts between mL and cm³ constantly.
Real-life problems in cooking, sports timing, travel and shopping all use these conversions.
Later algebra problems hide unit conversions inside word problems — spotting them early is half the battle.

Keep this revision handy — when an exam-style question feels confusing, the fix is often to write every quantity with its unit and convert to a single common unit first.

Physics relies on compound units like m/s and kg/m³.
Chemistry constantly converts mL to cm³ and L.
Word problems often hide a unit conversion in plain sight.
Always label numbers with their unit before calculating.

Sources: Cambridge Lower Secondary Mathematics curriculum framework. Last reviewed 2026-05-19.

Master this Topic

Worked examples, key facts and definitions, and the mistakes to watch out for — everything you need to feel confident with this topic.

Take this whole topic with you

Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Units of Measurements, ready to print or save as PDF.

Step-by-step worked examples — Units of Measurements

Step-by-step solutions for units of measurements, written exactly the way a tutor would explain them at the board.

1Converting a length to metres
Getting started• length, metric
Question
Convert $2.6\text{ km}$ into metres.
Step-by-step solution
1. Step 1
  There are $1000\text{ m}$ in $1\text{ km}$ , so multiply by $1000$ .
  $2.6 \text{ km} \times 1000$
2. Step 2
  Multiplying by $1000$ moves the decimal point three places to the right.
  $= 2600$
Answer
$2.6\text{ km} = 2600\text{ m}$ .
2Converting a mass to kilograms
Getting started• mass, metric
Question
A bag of flour has a mass of $750\text{ g}$ . Convert this into kilograms.
Step-by-step solution
1. Step 1
  There are $1000\text{ g}$ in $1\text{ kg}$ . Kilograms is the larger unit, so divide.
  $750 \div 1000$
2. Step 2
  Dividing by $1000$ moves the decimal point three places to the left.
  $= 0.75$
Answer
$750\text{ g} = 0.75\text{ kg}$ .
3Converting an area in m² to cm²
Building confidence• area, squared factor
Question
A poster has an area of $0.45\text{ m}^2$ . Find its area in $\text{cm}^2$ .
Step-by-step solution
1. Step 1
  The linear conversion is $1\text{ m} = 100\text{ cm}$ , so the area conversion squares the factor.
  $1 \text{ m}^2 = 100 \times 100 = 10{,}000 \text{ cm}^2$
2. Step 2
  Multiply by $10{,}000$ to convert from $\text{m}^2$ to the smaller $\text{cm}^2$ .
  $0.45 \times 10{,}000$
3. Step 3
  Work out the multiplication.
  $= 4500$
Answer
The poster has an area of $4500\text{ cm}^2$ .
4Finding a speed in km/h
Building confidence• speed, compound unit
Question
A cyclist rides $36\text{ km}$ in $1$ hour $30$ minutes. Find the average speed in $\text{km/h}$ .
Step-by-step solution
1. Step 1
  First write the time as a decimal of an hour: $1$ h $30$ min = $1.5$ h.
2. Step 2
  Use the speed formula $\text{speed} = \text{distance} \div \text{time}$ .
  $\text{speed} = 36 \div 1.5$
3. Step 3
  Work out the division.
  $= 24$
Answer
The cyclist's average speed is $24\text{ km/h}$ .
5Converting a volume in m³ to litres
Stretch• volume, cubed factor, capacity
Question
A fish tank has a volume of $0.18\text{ m}^3$ . How many litres of water does it hold?
Step-by-step solution
1. Step 1
  The linear conversion is $1\text{ m} = 100\text{ cm}$ , so the volume conversion cubes the factor.
  $1 \text{ m}^3 = 100^3 = 1{,}000{,}000 \text{ cm}^3$
2. Step 2
  Convert the volume to $\text{cm}^3$ .
  $0.18 \times 1{,}000{,}000 = 180{,}000 \text{ cm}^3$
3. Step 3
  Use the link $1\text{ cm}^3 = 1\text{ mL}$ , so $1000\text{ cm}^3 = 1\text{ L}$ .
  $180{,}000 \div 1000 = 180$
Answer
The fish tank holds $180\text{ L}$ of water.

Key Definitions and Keywords — Units of Measurements

The important words for units of measurements and what they mean — learn these so you can explain your thinking clearly.

Metric system
Key word
A system of units based on powers of 10, used worldwide for science and everyday measurement.
Kilo-
A prefix meaning $1000$ . So $1\text{ kg} = 1000\text{ g}$ .
Centi-
A prefix meaning $\frac{1}{100}$ . So $1\text{ cm} = \frac{1}{100}\text{ m}$ .
Milli-
A prefix meaning $\frac{1}{1000}$ . So $1\text{ mL} = \frac{1}{1000}\text{ L}$ .
Capacity
Key word
The amount of liquid a container can hold, measured in millilitres or litres.
Square units
Units used to measure area, such as $\text{mm}^2$ , $\text{cm}^2$ , $\text{m}^2$ and $\text{km}^2$ .
Cubic units
Key word
Units used to measure volume, such as $\text{cm}^3$ and $\text{m}^3$ . Note that $1\text{ cm}^3 = 1\text{ mL}$ .
Compound unit
Key word
A unit that combines two quantities, such as $\text{km/h}$ or $\text{g/cm}^3$ .
Speed
How quickly something moves, given by $\text{speed} = \text{distance} \div \text{time}$ .
Density
Key word
How much mass a material has per unit volume, given by $\text{density} = \text{mass} \div \text{volume}$ .
24-hour clock
A way of writing time that runs from $00\!:\!00$ to $23\!:\!59$ without needing am or pm.
Decimal hours
Writing time as a decimal of an hour. $0.5\text{ h} = 30\text{ min}$ , $0.25\text{ h} = 15\text{ min}$ .

Common Mistakes and Misconceptions — Units of Measurements

The slip-ups students most often make with units of measurements — and simple ways to avoid them.

✕Using the linear conversion factor instead of squaring it when converting area.
Why it happens
Students remember that $1\text{ m} = 100\text{ cm}$ and apply $\times 100$ to areas as well.
How to avoid it
Always square the linear factor for area: $1\text{ m}^2 = 100^2 = 10{,}000\text{ cm}^2$ .
✕Multiplying by $100$ or $10{,}000$ when converting volume from $\text{m}^3$ to $\text{cm}^3$ .
Why it happens
Students forget that volume needs the linear factor cubed.
How to avoid it
Cube the linear factor for volume: $1\text{ m}^3 = 100^3 = 1{,}000{,}000\text{ cm}^3$ .
✕Using time in minutes with a speed in $\text{km/h}$ without converting.
Why it happens
It is tempting to substitute the numbers straight into the formula and ignore the units.
How to avoid it
Make every quantity match the units of the answer. Convert $30$ minutes to $0.5$ hours before dividing.
✕Reading $1.5$ hours as $1$ hour $50$ minutes.
Why it happens
Students treat the decimal part as if time used base 100 instead of base 60.
How to avoid it
Multiply the decimal part by $60$ to get minutes: $0.5 \times 60 = 30$ , so $1.5\text{ h} = 1\text{ h}\,30\text{ min}$ .
✕Writing an answer without its unit.
Why it happens
Students focus on getting the number right and forget the unit at the end.
How to avoid it
Every measurement answer should include the unit — $5\text{ kg}$ , $12\text{ cm}$ , $30\text{ m/s}$ — not just a bare number.

Practice questions

Practice questions with step-by-step worked solutions. Try one before checking the method.

Practice quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Units of Measurements — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Units of Measurements

Short Study Notes in the form of Slides

Detailed Notes

What you’ll learn

1Converting a length to metres

2Converting a mass to kilograms

3Converting an area in m² to cm²

4Finding a speed in km/h

5Converting a volume in m³ to litres

Metric system

Kilo-

Centi-

Milli-

Capacity

Square units

Cubic units

Compound unit

Speed

Density

24-hour clock

Decimal hours

✕Using the linear conversion factor instead of squaring it when converting area.

✕Multiplying by 100100100 or 10,00010{,}00010,000 when converting volume from m3\text{m}^3m3 to cm3\text{cm}^3cm3.

✕Using time in minutes with a speed in km/h\text{km/h}km/h without converting.

✕Reading 1.51.51.5 hours as 111 hour 505050 minutes.

✕Writing an answer without its unit.

Practice questions

Practice quiz

Assess your understanding

Units of Measurements — frequently asked questions

✕Multiplying by $100$ or $10{,}000$ when converting volume from $\text{m}^3$ to $\text{cm}^3$ .

✕Using time in minutes with a speed in $\text{km/h}$ without converting.

✕Reading $1.5$ hours as $1$ hour $50$ minutes.