Units of measure
Section: Mensuration | Syllabus: Cambridge IGCSE Mathematics (0580)
Converting Between Units of Length, Mass and Capacity
Metric units of length, mass and capacity are all based on powers of 10, making conversion a matter of multiplying or dividing by the correct power of 10.
- Length: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm
- Mass: 1 kg = 1000 g, 1 g = 1000 mg
- Capacity: 1 litre = 1000 millilitres
- To convert to a smaller unit, multiply; to convert to a larger unit, divide
Worked Example: Converting Length Through Multiple Units
- Question: Convert 3.5 km to cm.
- Step 1: Convert km to m: 3.51000=3500 m
- Step 2: Convert m to cm: 3500100=350\,000 cm
- Answer: 350 000 cm
Worked Example: Converting Mass to a Larger Unit
- Question: Convert 4200 g to kg.
- Step 1: 1 kg = 1000 g, so divide by 1000
- Step 2: 42001000=4.2
- Answer: 4.2 kg
Common Mistakes
MistakeMultiplying when converting to a larger unit, or dividing when converting to a smaller unit - the opposite of what's needed
Fixconverting to a smaller unit always means more of that unit, so multiply; converting to a larger unit means fewer of it, so divide
MistakeUsing the wrong conversion factor, e.g. treating 1 m as 1000 cm instead of 100 cm
Fixlearn the exact factors precisely - length steps are ×10 or ×100 depending on the units involved, not always the same number
Converting Between Units of Area and Volume
Converting units of area and volume is not as simple as converting length - the conversion factor must be squared for area, or cubed for volume, since each dimension is converted separately.
- Since 1 m = 100 cm, 1 m^2=100^2 cm^2=10\,000 cm^2 (the length factor is squared for area)
- Since 1 m = 100 cm, 1 m^3=100^3 cm^3=1\,000\,000 cm^3 (the length factor is cubed for volume)
- 1 litre = 1000 cm³, a very useful conversion linking capacity and volume
- To convert cm² to m², divide by 10 000; to convert cm³ to m³, divide by 1 000 000
Worked Example: Converting Volume to Capacity
- Question: Convert 45 cm³ to litres.
- Step 1: 1 litre = 1000 cm³
- Step 2: 451000=0.045
- Answer: 0.045 litres
Worked Example: Converting Area Between Units
- Question: Convert 5.2 m² to cm².
- Step 1: 1 m² = 10 000 cm²
- Step 2: 5.210\,000=52\,000
- Answer: 52 000 cm²
Common Mistakes
MistakeUsing the same conversion factor for area as for length, e.g. ×100 instead of ×10 000 when converting m² to cm²
Fixalways square the length conversion factor for area (×100² = ×10 000), and cube it for volume (×100³ = ×1 000 000)
MistakeConfusing which direction to convert between litres and cm³, e.g. multiplying by 1000 instead of dividing
Fixsince 1 litre is a larger unit than 1 cm³, converting cm³ to litres means dividing by 1000, not multiplying
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