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Compound units and converting measures
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Speed, density and price per item are compound units: they combine two measures. Converting units carefully stops easy mistakes.
Speed and density
Speed = distance ÷ time (km/h, m/s).
Density = mass ÷ volume (g/cm3).
Rearrange as needed: distance = speed × time, mass = density × volume.
Time in minutes must be changed to hours for km/h: 45 minutes = 0.75 hours.
Density = mass ÷ volume (g/cm3).
Rearrange as needed: distance = speed × time, mass = density × volume.
Time in minutes must be changed to hours for km/h: 45 minutes = 0.75 hours.
Converting lengths, areas and volumes
1 m = 100 cm, but 1 m2 = 100 × 100 = 10 000 cm2 and 1 m3 = 1 000 000 cm3.
1 litre = 1 000 cm3 = 1 000 ml.
1 kg = 1 000 g.
1 litre = 1 000 cm3 = 1 000 ml.
1 kg = 1 000 g.
Time
Time is not decimal. 2.4 hours = 2 hours + 0.4 × 60 minutes = 2 hours 24 minutes.
To change m/s into km/h, multiply by 3 600 (seconds in an hour) then divide by 1 000: 20 m/s = 72 km/h.
To change m/s into km/h, multiply by 3 600 (seconds in an hour) then divide by 1 000: 20 m/s = 72 km/h.
A car travels at 48 km/h for 45 minutes. How far does it go?
- 45 minutes = 0.75 hours
- distance = speed × time = 48 × 0.75
Answer: 36 km
Speed = distance ÷ time and density = mass ÷ volume. Make the units match before you calculate, and remember that area and volume conversions use squared and cubed factors.
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