3.5 Units and measures
Units and measures
Everything on units and measures that can come up in the WJEC GCSE Mathematics and Numeracy, in all three units. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
Practise units and measures free
A worked example
Metric units · [1 mark]
Change 7.1 kg into g.
- B1× 1000 = 7100 g
The exam skills (12)
Metric units
- Know the links: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 l = 1000 ml.
- Big unit to small unit: multiply. Small to big: divide.
- Check the answer makes sense.
Watch out: Dividing when changing km into m. The number should get bigger.
Time
- Count on to the next hour, then on to the end time.
- There are 60 minutes in an hour, not 100.
- Change hours and minutes into what the question asks for.
Watch out: Using a calculator: 1.5 hours is 1 hour 30 minutes, not 1 hour 50.
Speed, distance, time
- Speed = distance ÷ time. Distance = speed × time. Time = distance ÷ speed.
- Make the units match (minutes into hours by ÷ 60).
- Give the units: km/h, m/s, mph.
Watch out: Using 30 minutes as 0.3 hours. It is 0.5 hours.
Reading scales
- Find two numbered marks next to each other.
- Divide the gap by the number of small divisions between them.
- Count on from the last number to the arrow.
Watch out: Assuming every small division is 1.
Density
- Density = mass ÷ volume.
- Mass = density × volume. Volume = mass ÷ density.
- Give the units: g/cm³ goes with grams and cm³.
Watch out: Multiplying when you should divide. Use the formula triangle.
Area and volume units
- Square the conversion: 1 m = 100 cm, so 1 m² = 100² = 10,000 cm².
- Cube it for volume: 1 m³ = 1,000,000 cm³.
- Then multiply or divide as normal.
Watch out: Using 100 for m² to cm². It is 10,000.
Imperial units
- Use the conversion given, e.g. 5 miles ≈ 8 km.
- Work out the scale: how many lots of 5 miles?
- Multiply by 8.
Watch out: Multiplying by 8 ÷ 5 the wrong way round. Check: km numbers are bigger than miles.
Time zones
- Find the arrival time in UK time first: add the flight time.
- Ahead of the UK: add the difference. Behind: take it away.
- Write the answer in the 24-hour clock.
Watch out: Adding the difference for a place that is behind the UK.
Population density
- Population density = number of people ÷ area.
- People = density × area. Area = people ÷ density.
- Units: people per km².
Watch out: Dividing the area by the population.
Compound units
- m/s to km/h: multiply by 3600 (seconds in an hour), then ÷ 1000 (m in a km).
- That is the same as × 3.6.
- Check: km/h numbers are bigger.
Watch out: Only doing one of the two conversions.
Pressure
- Pressure = force ÷ area.
- Make sure the area is in the units asked for.
- Give units: N/m² (newtons per square metre).
Watch out: Multiplying force by area.
Rates of flow
- Find the volume of the tank, then change it into litres (1 m³ = 1000 litres).
- Time = volume ÷ rate.
- Change the time into the units asked for.
Watch out: Forgetting to change m³ into litres before dividing.
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