Compound unit conversion

Objective. Convert rates across time, length, area and volume units.

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Learn: the key idea

Compound unit conversion changes rates such as speed, density or flow between different time, length, area or volume units, by converting each part of the rate separately. To convert km/h to m/s, multiply by 1000 (km to m) and divide by 3600 (hours to seconds), since 1 km/h = 1000/3600 m/s. For area and volume conversions, remember that converting 1m to 100cm means 1m²=100²cm²=10000cm², and 1m³=100³cm³=1,000,000cm³, because each dimension is scaled. To convert 72 km/h to m/s: 72×1000÷3600=20 m/s. Always convert the numerator and denominator units separately before combining them into the new rate.

Worked example

Convert a speed of 90 km/h into metres per second.

1 $Convert km to m: 90 km = 90,000 m$
2 $Convert hours to seconds: 1 hour = 3600 seconds$
3 $Divide: speed = 90,000 \div 3600$
4 $Calculate: 90,000 \div 3600 = 25 m/s$

Answer: 25 m/s

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Common mistake. Pupils convert units for area or volume using the same scale factor as length, forgetting to square or cube it. Converting 2m² to cm² by multiplying by 100 gives 200cm² instead of the correct 20000cm² (multiplying by 100²). Always square the conversion factor for area and cube it for volume.

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