How do I know whether to multiply or divide in a unit conversion?

Ask whether you are moving to a smaller or larger unit. Moving to a smaller unit usually makes the numerical value larger, while moving to a larger unit usually makes it smaller.

Why is $1\text{ m}^2$ equal to $10{,}000\text{ cm}^2$?

Because $1\text{ m}=100\text{ cm}$ and an area conversion squares that factor: $(100)^2=10{,}000$.

How do I convert cubic metres to cubic centimetres?

Cube the length conversion. Since $1\text{ m}=100\text{ cm}$, $1\text{ m}^3=(100)^3\text{ cm}^3=1{,}000{,}000\text{ cm}^3$.

Is $1.4$ hours equal to $1$ hour $40$ minutes?

No. Convert the decimal part using $60$ minutes per hour: $0.4\times60=24$. Therefore, $1.4$ hours is $1$ hour $24$ minutes.

Should I convert units before using a formula?

Yes, if the given measurements use different or unsuitable units. Convert them into compatible units first, then substitute into the formula and state the resulting unit.

Common Unit Conversion Mistakes in GCSE Maths

A unit conversion can look almost too easy. Multiply by $100$ , divide by $1{,}000$ , write down the answer and move on. Yet these questions regularly cost marks because one small decision, often made too quickly, changes the answer completely.

The common mistakes with unit conversions in GCSE Maths are usually not caused by difficult arithmetic. Students reverse conversion factors, treat area like length, treat time like a decimal system or forget to make units consistent before using a formula.

Imagine a student reviewing a marked paper. The method is mostly right, but the units tell another story. By correcting each error carefully, the student builds a routine that can be used across Edexcel, AQA, OCR and Eduqas papers.

The unit conversion checklist

Before calculating, ask:

What unit do I have?
What unit does the question require?
Am I converting length, area, volume, mass or time?
Should the numerical value become larger or smaller?
Do all measurements use compatible units?
Have I written the final unit?

The central idea is simple: converting a measurement changes its numerical representation, not the actual quantity. A length of $m2\text{ m}$ and a length of $cm200\text{ cm}$ describe the same distance.

You can review that principle in the Metric Conversions lesson or use the Metric Conversions revision guide alongside these examples.

Mistake: using the conversion factor backwards

The student wants to convert $m3.6\text{ m}$ into centimetres. They remember the number $100$ , but divide:

3.6 \div 100 = 0.036

Why it happens

A remembered conversion factor is not a complete method. You must also decide which operation makes sense.

Since

cm,1\text{ m}=100\text{ cm},

one metre contains many centimetres. The number of centimetres should therefore be larger than the number of metres.

Correct method

3.6 \times 100=360

Therefore,

cm.3.6\text{ m}=360\text{ cm}.

Use direction as a check:

larger unit to smaller unit: the numerical value normally increases;
smaller unit to larger unit: the numerical value normally decreases.

This check is often faster than trying to remember an arrow diagram under exam pressure.

Mistake: applying a length conversion to area

Next, the student converts $m22.4\text{ m}^2$ into square centimetres. They multiply by $100$ and obtain $cm2240\text{ cm}^2$ .

Why it happens

The conversion $cm1\text{ m}=100\text{ cm}$ concerns one-dimensional length. Area has two dimensions, so the conversion factor must be squared.

Correct method

Start with the length conversion:

cm.1\text{ m}=100\text{ cm}.

Square both sides:

cm2.1\text{ m}^2=(100\text{ cm})^2=10{,}000\text{ cm}^2.

Now convert:

2.4 \times 10{,}000=24{,}000.

Therefore,

cm2.2.4\text{ m}^2=24{,}000\text{ cm}^2.

The exponent belongs to the conversion factor as well as the unit. The Conversions and Units revision guide gives further support with length, area, volume and related conversions.

Mistake: forgetting to cube a volume conversion

The same student sees $m30.5\text{ m}^3$ and again reaches for $100$ . Even squaring it would not be enough.

Why it happens

Volume has three dimensions. If each dimension is converted from metres to centimetres, the factor $100$ is used three times.

Correct method

cm3.1\text{ m}^3=(100\text{ cm})^3=1{,}000{,}000\text{ cm}^3.

Then

0.5 \times 1{,}000{,}000=500{,}000.

cm3.0.5\text{ m}^3=500{,}000\text{ cm}^3.

A useful pattern is:

Measurement	Conversion factor
Length	Use the factor once
Area	Square the factor
Volume	Cube the factor

This is one of the most important distinctions in unit conversions GCSE questions.

A student checks a giant pencil with a tiny ruler while another asks whether they checked the units

Mistake: treating time as base ten

The student writes $1.5$ hours as $1$ hour $50$ minutes. It feels natural because $0.5$ resembles fifty hundredths.

Why it happens

Most metric conversions use powers of ten, but hours and minutes do not. One hour contains $60$ minutes.

Correct method

Keep the whole hour, then convert the decimal part:

0.5 \times 60=30.

Therefore,

minutes.1.5\text{ hours}=1\text{ hour }30\text{ minutes}.

For $2$ hours $18$ minutes as decimal hours, divide the minutes by $60$ :

18 \div 60=0.3.

Therefore,

hours.2\text{ hours }18\text{ minutes}=2.3\text{ hours}.

The reverse check is valuable:

0.3 \times 60=18.

Now that you have the method, use the Conversions and Units lesson and its practice cards to make spotting these errors more automatic.

Mistake: calculating with mixed units

The student is asked for the area of a rectangle measuring $m1.8\text{ m}$ by $cm40\text{ cm}$ . They multiply immediately:

1.8 \times 40=72.

The arithmetic is correct, but the calculation combines metres and centimetres. The result has no useful standard area unit.

Correct method

Convert before applying the area formula. In centimetres,

cm.1.8\text{ m}=180\text{ cm}.

Then

cm2.\text{area}=180 \times 40=7{,}200\text{ cm}^2.

Alternatively, convert $cm40\text{ cm}$ to metres:

m,40\text{ cm}=0.4\text{ m},

m2.\text{area}=1.8 \times 0.4=0.72\text{ m}^2.

These answers agree because

cm2.0.72\text{ m}^2=7{,}200\text{ cm}^2.

The habit to remember is: convert first, substitute second.

Mistake: converting only part of a compound unit

Suppose a car travels at $km/h72\text{ km/h}$ and the question asks for metres per second. The student converts kilometres to metres but leaves hours unchanged.

Why it happens

A compound unit contains more than one unit. Both parts must match the requested form.

Correct method

Use

m1\text{ km}=1{,}000\text{ m}

and

s.1\text{ hour}=3{,}600\text{ s}.

Then

m/s.72\text{ km/h}=\frac{72\times1{,}000}{3{,}600}\text{ m/s}=20\text{ m/s}.

Notice that the time conversion appears in the denominator. Writing the fraction explicitly helps prevent an accidental multiplication by $3{,}600$ .

For broader practice with conversion graphs and speed units, visit the Conversions and Units topic page. OCR students can use the matching OCR Conversions and Units lesson.

Common mistakes to check before moving on

The student's lost marks can now be reduced to six checks:

Do not multiply or divide until you know whether the answer should grow or shrink.
Do not use a length factor unchanged for area or volume.
Do not treat minutes as hundredths of an hour.
Do not substitute mixed units into a formula.
Do not convert only one part of a compound unit.
Do not leave the final number without its unit.

An answer of $500$ is incomplete if the question requires $g500\text{ g}$ . Units are part of the mathematical meaning, not decoration added afterwards.

Exam-style practice

Try these without looking back. Show each conversion step and include the final unit.

Convert $km4.7\text{ km}$ to metres.
Convert $cm236{,}000\text{ cm}^2$ to square metres.
Convert $m30.08\text{ m}^3$ to cubic centimetres.
Write $3.25$ hours in hours and minutes.
A rectangle measures $m2.5\text{ m}$ by $cm60\text{ cm}$ . Find its area in square metres.
Convert $km/h54\text{ km/h}$ to metres per second.

Answers

$m4{,}700\text{ m}$
$m23.6\text{ m}^2$
$cm380{,}000\text{ cm}^3$
$3$ hours $15$ minutes
$m21.5\text{ m}^2$
$m/s15\text{ m/s}$

When checking, do not look only at the final number. Identify the conversion factor, operation and unit. That is where most unit conversions mistakes begin.

Turn the checks into reliable marks

The student in this article did not need a new trick. They needed a repeatable sequence: name the units, choose the factor, account for dimensions, calculate and check whether the answer is sensible. Knowing that sequence helps, but following it consistently takes practice.

Your turn. Start the matching Maths Genie Metric Conversions lesson, then use the topic Question Bank to practise recognising and fixing the unit conversion errors that cost marks.

The unit conversion checklist

Before calculating, ask:

What unit do I have?
What unit does the question require?
Am I converting length, area, volume, mass or time?
Should the numerical value become larger or smaller?
Do all measurements use compatible units?
Have I written the final unit?

You can review that principle in the Metric Conversions lesson or use the Metric Conversions revision guide alongside these examples.

Mistake: using the conversion factor backwards

The student wants to convert $m3.6\text{ m}$ into centimetres. They remember the number $100$ , but divide:

3.6 \div 100 = 0.036

Why it happens

A remembered conversion factor is not a complete method. You must also decide which operation makes sense.

Since

cm,1\text{ m}=100\text{ cm},

one metre contains many centimetres. The number of centimetres should therefore be larger than the number of metres.

Correct method

3.6 \times 100=360

Therefore,

cm.3.6\text{ m}=360\text{ cm}.

Use direction as a check:

larger unit to smaller unit: the numerical value normally increases;
smaller unit to larger unit: the numerical value normally decreases.

This check is often faster than trying to remember an arrow diagram under exam pressure.

Mistake: applying a length conversion to area

Next, the student converts $m22.4\text{ m}^2$ into square centimetres. They multiply by $100$ and obtain $cm2240\text{ cm}^2$ .

Why it happens

The conversion $cm1\text{ m}=100\text{ cm}$ concerns one-dimensional length. Area has two dimensions, so the conversion factor must be squared.

Correct method

Start with the length conversion:

cm.1\text{ m}=100\text{ cm}.

Square both sides:

cm2.1\text{ m}^2=(100\text{ cm})^2=10{,}000\text{ cm}^2.

Now convert:

2.4 \times 10{,}000=24{,}000.

Therefore,

cm2.2.4\text{ m}^2=24{,}000\text{ cm}^2.

The exponent belongs to the conversion factor as well as the unit. The Conversions and Units revision guide gives further support with length, area, volume and related conversions.

Mistake: forgetting to cube a volume conversion

The same student sees $m30.5\text{ m}^3$ and again reaches for $100$ . Even squaring it would not be enough.

Why it happens

Volume has three dimensions. If each dimension is converted from metres to centimetres, the factor $100$ is used three times.

Correct method

cm3.1\text{ m}^3=(100\text{ cm})^3=1{,}000{,}000\text{ cm}^3.

Then

0.5 \times 1{,}000{,}000=500{,}000.

cm3.0.5\text{ m}^3=500{,}000\text{ cm}^3.

A useful pattern is:

Measurement	Conversion factor
Length	Use the factor once
Area	Square the factor
Volume	Cube the factor

This is one of the most important distinctions in unit conversions GCSE questions.

A student checks a giant pencil with a tiny ruler while another asks whether they checked the units

Mistake: treating time as base ten

The student writes $1.5$ hours as $1$ hour $50$ minutes. It feels natural because $0.5$ resembles fifty hundredths.

Why it happens

Most metric conversions use powers of ten, but hours and minutes do not. One hour contains $60$ minutes.

Correct method

Keep the whole hour, then convert the decimal part:

0.5 \times 60=30.

Therefore,

minutes.1.5\text{ hours}=1\text{ hour }30\text{ minutes}.

For $2$ hours $18$ minutes as decimal hours, divide the minutes by $60$ :

18 \div 60=0.3.

Therefore,

hours.2\text{ hours }18\text{ minutes}=2.3\text{ hours}.

The reverse check is valuable:

0.3 \times 60=18.

Now that you have the method, use the Conversions and Units lesson and its practice cards to make spotting these errors more automatic.

Mistake: calculating with mixed units

The student is asked for the area of a rectangle measuring $m1.8\text{ m}$ by $cm40\text{ cm}$ . They multiply immediately:

1.8 \times 40=72.

The arithmetic is correct, but the calculation combines metres and centimetres. The result has no useful standard area unit.

Correct method

Convert before applying the area formula. In centimetres,

cm.1.8\text{ m}=180\text{ cm}.

Then

cm2.\text{area}=180 \times 40=7{,}200\text{ cm}^2.

Alternatively, convert $cm40\text{ cm}$ to metres:

m,40\text{ cm}=0.4\text{ m},

m2.\text{area}=1.8 \times 0.4=0.72\text{ m}^2.

These answers agree because

cm2.0.72\text{ m}^2=7{,}200\text{ cm}^2.

The habit to remember is: convert first, substitute second.

Mistake: converting only part of a compound unit

Suppose a car travels at $km/h72\text{ km/h}$ and the question asks for metres per second. The student converts kilometres to metres but leaves hours unchanged.

Why it happens

A compound unit contains more than one unit. Both parts must match the requested form.

Correct method

Use

m1\text{ km}=1{,}000\text{ m}

and

s.1\text{ hour}=3{,}600\text{ s}.

Then

m/s.72\text{ km/h}=\frac{72\times1{,}000}{3{,}600}\text{ m/s}=20\text{ m/s}.

Notice that the time conversion appears in the denominator. Writing the fraction explicitly helps prevent an accidental multiplication by $3{,}600$ .

For broader practice with conversion graphs and speed units, visit the Conversions and Units topic page. OCR students can use the matching OCR Conversions and Units lesson.

Common mistakes to check before moving on

The student's lost marks can now be reduced to six checks:

Do not multiply or divide until you know whether the answer should grow or shrink.
Do not use a length factor unchanged for area or volume.
Do not treat minutes as hundredths of an hour.
Do not substitute mixed units into a formula.
Do not convert only one part of a compound unit.
Do not leave the final number without its unit.

An answer of $500$ is incomplete if the question requires $g500\text{ g}$ . Units are part of the mathematical meaning, not decoration added afterwards.

Exam-style practice

Try these without looking back. Show each conversion step and include the final unit.

Convert $km4.7\text{ km}$ to metres.
Convert $cm236{,}000\text{ cm}^2$ to square metres.
Convert $m30.08\text{ m}^3$ to cubic centimetres.
Write $3.25$ hours in hours and minutes.
A rectangle measures $m2.5\text{ m}$ by $cm60\text{ cm}$ . Find its area in square metres.
Convert $km/h54\text{ km/h}$ to metres per second.

Answers

$m4{,}700\text{ m}$
$m23.6\text{ m}^2$
$cm380{,}000\text{ cm}^3$
$3$ hours $15$ minutes
$m21.5\text{ m}^2$
$m/s15\text{ m/s}$

When checking, do not look only at the final number. Identify the conversion factor, operation and unit. That is where most unit conversions mistakes begin.

Turn the checks into reliable marks

Your turn. Start the matching Maths Genie Metric Conversions lesson, then use the topic Question Bank to practise recognising and fixing the unit conversion errors that cost marks.

The unit conversion checklist

Mistake: using the conversion factor backwards

Why it happens

Correct method

Mistake: applying a length conversion to area

Why it happens

Correct method

Mistake: forgetting to cube a volume conversion

Why it happens

Correct method

Mistake: treating time as base ten

Why it happens

Correct method

Mistake: calculating with mixed units

Correct method

Mistake: converting only part of a compound unit

Why it happens

Correct method

Common mistakes to check before moving on

Exam-style practice

Answers

Turn the checks into reliable marks

Frequently Asked Questions

How do I know whether to multiply or divide in a unit conversion?

How do I know whether to multiply or divide in a unit conversion?

Why is $1\text{ m}^2$ equal to $10{,}000\text{ cm}^2$?

Why is $1\text{ m}^2$ equal to $10{,}000\text{ cm}^2$?

How do I convert cubic metres to cubic centimetres?

How do I convert cubic metres to cubic centimetres?

Is $1.4$ hours equal to $1$ hour $40$ minutes?

Is $1.4$ hours equal to $1$ hour $40$ minutes?

Should I convert units before using a formula?

Should I convert units before using a formula?

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The unit conversion checklist

Mistake: using the conversion factor backwards

Why it happens

Correct method

Mistake: applying a length conversion to area

Why it happens

Correct method

Mistake: forgetting to cube a volume conversion

Why it happens

Correct method

Mistake: treating time as base ten

Why it happens

Correct method

Mistake: calculating with mixed units

Correct method

Mistake: converting only part of a compound unit

Why it happens

Correct method

Common mistakes to check before moving on

Exam-style practice

Answers

Turn the checks into reliable marks

Frequently Asked Questions

How do I know whether to multiply or divide in a unit conversion?

How do I know whether to multiply or divide in a unit conversion?

Why is $1\text{ m}^2$ equal to $10{,}000\text{ cm}^2$?

Ready to breeze through your GCSEs?

Ready to breeze through your GCSEs?