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cm³ is converted to m³ by cubing the length conversion: 1 cm = 0.01 m, so 1 cm³ = (0.01 m)³ = 0.000001 m³. Free GCSE Maths notes and 14 FAQs.
Converting Between Standard and Compound Units is part of Units, Scale and Similarity in GCSE AQA Higher Maths.
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cm³ is converted to m³ by cubing the length conversion: 1 cm = 0.01 m, so 1 cm³ = (0.01 m)³ = 0.000001 m³. Free GCSE Maths notes and 14 FAQs.
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Use this lesson to stay inside Units, Scale and Similarity while connecting the detail back to the wider Ratio, proportion and rates of change topic.
Read the core explanations from Converting Between Standard and Compound Units before testing yourself from memory.
You're buying carpet for your bedroom. The room is 3.5m by 4.2m, but the carpet shop prices are in square feet. Without unit conversion, you're stuck.
Unit conversion isn't just academic - it's everywhere. Speed limits switch between mph and km/h. Recipes use grams and ounces. Medicine doses depend on body weight in kilograms.
In GCSE exams, unit conversion questions are mark-winners if you know the method. They're mark-losers if you panic about the arithmetic. Let's fix that.
Standard units are your building blocks. Master these conversions and everything else follows. The key insight: each conversion has a multiplication factor.
Length conversions work in powers of 10. From kilometres down to millimetres, each step multiplies or divides by 10, 100, or 1000.
Time conversions don't follow the decimal pattern. Hours to minutes uses 60, minutes to seconds uses 60 again. Days to hours uses 24.
Mass and volume follow the decimal system like length. Kilograms to grams uses 1000. Litres to millilitres also uses 1000.
The secret to unit conversion is the multiplication method. You multiply by a fraction that equals 1, so the quantity stays the same but the units change.
Worked example: Converting 3.2 km to metres
A running track is 3.2 km long. Express this distance in metres.
Answer: 3200 m
Converting to smaller units means multiplying by a number greater than 1. Converting to larger units means multiplying by a number less than 1 (or dividing).
Worked example: Converting 4500 g to kilograms
A bag of flour weighs 4500 g. What is this mass in kilograms?
Answer: 4.5 kg
Area and volume conversions are trickier because they involve squared and cubed units. When you convert length, the conversion factor gets squared for area and cubed for volume.
Worked example: Converting 5 m² to cm²
A table top has area 5 m². Express this area in cm².
Answer: 50,000 cm²
Compound units combine two or more standard units. Speed combines distance and time. Density combines mass and volume. Rates of pay combine money and time.
The word 'per' means 'divided by'. So 60 miles per hour means 60 miles ÷ 1 hour. This gives us the conversion method for compound units.
Worked example: Converting 72 km/h to m/s
A car travels at 72 km/h. What is this speed in m/s?
Answer: 20 m/s
There's a quick method for km/h to m/s: divide by 3.6. This works because 1 km/h = 1000m ÷ 3600s = 1/3.6 m/s.
Density problems often require converting both mass and volume units. The key is to convert each part separately, then combine them.
Worked example: Density Conversion: g/cm³ to kg/m³
Gold has density 19.3 g/cm³. Express this in kg/m³.
Answer: 19,300 kg/m³
Unit conversion appears everywhere in daily life. Cooking recipes, fuel efficiency, medicine doses, and international travel all require switching between different measurement systems.
Fuel efficiency shows the difference between metric and imperial thinking. UK cars show miles per gallon, but European cars show litres per 100 kilometres. These measure opposite things.
Worked example: Comparing fuel efficiency units
A car does 35 miles per gallon. A European car does 8 litres per 100 km. Which is more efficient?
Answer: Both cars are equally efficient at 8 litres per 100 km
Medicine doses depend on body weight, usually given as mg per kg. A 70 kg adult needs different doses than a 20 kg child.
Construction and DIY projects mix metric and imperial units. Timber comes in imperial sizes (2×4 inches) but room measurements use metres. Conversion skills prevent expensive mistakes.
Unit conversion questions are mark-winners in GCSE exams, but only if you avoid the common traps. Examiners love to test whether you really understand the process.
The biggest trap is mixing up when to multiply and when to divide. Remember: converting to smaller units means the number gets bigger. Converting to larger units means the number gets smaller.
Area and volume conversions catch many students. They forget to square or cube the conversion factor. A common error is converting 1 m² to 100 cm² instead of 10,000 cm².
Speed conversion questions often use the quick methods. Know that km/h ÷ 3.6 = m/s, and m/s × 3.6 = km/h. But be ready to show the full method if asked.
Practice with mixed unit problems. Examiners combine unit conversion with other topics like percentages, ratios, or problem solving. Master the conversion skills first, then tackle the combinations.
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Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
cm³ is converted to m³ by cubing the length conversion: 1 cm = 0.01 m, so 1 cm³ = (0.01 m)³ = 0.000001 m³. Volume conversions always cube the length factor.
To convert m² to cm², square the length conversion factor: 1 m = 100 cm, so 1 m² = 10,000 cm². A table top of 5 m² is 5 × 10,000 = 50,000 cm²; a common error is using 100 instead of 10,000.
Miles per gallon is compared with litres per 100 km by converting both parts: 35 miles ≈ 56 km and 1 gallon ≈ 4.5 litres, giving 4.5 ÷ 56 = 0.08 litres per km. That is 8 litres per 100 km, the same as a car using 8 litres per 100 km.
A conversion factor is a fraction equal to 1 that changes units without changing the actual quantity, such as 1000 m/1 km. For example, 3.2 km × 1000 m/1 km = 3200 m, because the km units cancel.
4500 g is 4.5 kg. Since 1000 g = 1 kg, 4500 ÷ 1000 = 4.5, and converting to a larger unit makes the number smaller.
A rate is a compound unit showing how one quantity changes with respect to another, always written as 'something per something else', such as miles per hour or pounds per kilogram. The word per means divided by.
Convert the mass and volume units separately, then combine them. Gold's density of 19.3 g/cm³ is 0.0193 kg per 0.000001 m³, and 0.0193 ÷ 0.000001 = 19,300 kg/m³.
Divide by 3.6 to convert km/h to m/s, and multiply by 3.6 to convert back. This works because 1 km/h = 1000 m ÷ 3600 s = 1/3.6 m/s, so 72 km/h is 72,000 ÷ 3600 = 20 m/s.
Converting to a smaller unit makes the number bigger, so multiply; converting to a larger unit makes the number smaller, so divide. For example, 3.2 km = 3200 m, while 4500 g = 4500 ÷ 1000 = 4.5 kg.
3.2 km is 3200 m. Using the conversion factor 1000 m/1 km, 3.2 km × 1000 = 3200 m, and the km units cancel to leave metres.
72 km/h is 20 m/s. Converting the distance gives 72 × 1000 = 72,000 m per hour, and dividing by 3600 seconds gives 72,000 ÷ 3600 = 20 m/s; the quick method is 72 ÷ 3.6 = 20.
m/s is converted to km/h by multiplying by 3.6, and km/h is converted to m/s by dividing by 3.6. This works because 1 km/h = 1000 m ÷ 3600 s = 1/3.6 m/s.
The conversion factor is squared for area because area is length × length. Since 1 m = 100 cm, 1 m² = (100 cm)² = 10,000 cm², so 5 m² = 50,000 cm²; using 100 instead of 10,000 is a common error.
Time conversions do not follow the decimal pattern: hours to minutes uses 60, minutes to seconds uses 60 again, and days to hours uses 24. So 1 hour = 3600 seconds.