Mathematics (Core)Exam code: 0580
Time, Currency and Conversions
Number
The conversions to know
- Metric conversions all work by multiplying or dividing by a power of ten
| Measure | Conversions |
|---|---|
| Length | 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m |
| Mass | 1 g = 1000 mg, 1 kg = 1000 g, 1 tonne = 1000 kg |
| Capacity | 1 litre = 1000 ml, 1 cl = 10 ml |
| Volume to capacity | 1 ml = 1 cm³, 1 litre = 1000 cm³, 1 m³ = 1000 litres |
- Decide between multiplying and dividing by asking whether the count of units should go up or down
- Changing to a smaller unit gives a bigger number, so multiply; changing to a larger unit gives a smaller number, so divide
- Awkward conversions are safer in stages, so centimetres to kilometres goes through metres first
Worked example
Converting length, mass and capacity
Convert 4.6 km into centimetres, 750 g into kilograms and 1850 cm³ into litres.
Solution:
- A centimetre is smaller than a kilometre, so the number of units goes up: multiply
- Go through metres: 4.6 km = 4.6 × 1000 = 4600 m
- Then 4600 m = 4600 × 100 = 460 000 cm
- A kilogram is larger than a gram, so the number of units goes down: divide by 1000
- 750 g = 750 ÷ 1000 = 0.75 kg
- A litre is 1000 cm³, so changing cm³ into litres is changing to the larger unit: divide by 1000
- 1850 cm³ = 1850 ÷ 1000 = 1.85 litres
- Check the sizes: 1 km is 100 000 cm, so 4.6 km must be several hundred thousand centimetres, and 750 g is less than a kilogram
Squared and cubed units
- Area units are squared, so the conversion factor is squared too
- Volume units are cubed, so the conversion factor is cubed
- 1 cm² = 10² mm² = 100 mm²
- 1 m² = 100² cm² = 10 000 cm²
- 1 km² = 1000² m² = 1 000 000 m²
- 1 cm³ = 10³ mm³ = 1000 mm³
- 1 m³ = 100³ cm³ = 1 000 000 cm³
- Picture a square metre as a square measuring 100 cm by 100 cm, which makes the 10 000 obvious rather than something to memorise
- The syllabus names conversion between area units and between volume and capacity explicitly, so both are examinable
Worked example
Converting an area
Convert 2.5 m² into cm², and 45 000 cm² into m².
Solution:
- One metre is 100 cm, so one square metre is 100 × 100 = 10 000 cm²
- Changing to the smaller unit means multiplying
- 2.5 × 10 000 = 25 000 cm²
- Going the other way means dividing by the same factor
- 45 000 ÷ 10 000 = 4.5 m²
- Check: 4.5 × 10 000 = 45 000