Metric and compound-unit conversions · Higher
مُقدَّم| English | المعنى |
|---|---|
| conversion factor/kənˈvɜːʃn ˈfæktə/ | عامل التحويل |
Why must the factor be squared?
- A floor tile measures 0.4 m by 0.4 m. Why is its area not 0.16×100 square centimetres?
- This lesson studies conversion factor 换算因子: The multiplier that expresses the same quantity in another unit.
The method
- Convert each dimension.
- Since 1 m=100 cm, 1 m²=10,000 cm² and 1 m³=1,000,000 cm³.
- Also 1 litre=1000 cm³, 1 kg=1000 g and 1 hour=3600 seconds.
- For a compound unit convert numerator and denominator, keeping the physical quantity unchanged.
Why is 1 m² equal to 10,000 cm² rather than 100 cm²?
الصعوبة 1/5 · 100 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
A 1 m by 1 m square is 100 cm by 100 cm, holding 10,000 cm². Converting only once confuses a length factor with an area factor; volumes cube it.
A worked case
0.4 m=40 cm, so the tile area is 40×40=1600 cm², agreeing with 0.16×10,000. A 0.002 m³ container holds 2000 cm³=2 litres. A speed of 72 km/h is 72,000/3600=20 m/s. Write the units at each stage so the conversion can be checked.
Metric and compound-unit conversions
Convert each dimension
Compare the model with the worked case and explain one change.
Convert 0.16 m² to cm².
الصعوبة 2/5 · 140 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
Multiply 0.16 by 100²: 1600.
Where it goes wrong
- The area multiplier is the square of the length multiplier; the volume multiplier is its cube.
- An hour is 60 minutes, not 100.
- Converting only the numerator of a speed gives an inconsistent unit.
Not true: To convert square metres to square centimetres, multiply by 100. 1 m²=100 cm×100 cm=10 000 cm², so multiply by 10 000.
Convert 0.002 m³ to litres.
الصعوبة 2/5 · 140 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
0.002×1,000,000=2000 cm³; divide by 1000 for 2 litres.
1 m²=100 cm×100 cm=10 000 cm², so multiply by 10 000.
الصعوبة 1/5 · 100 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
True. 1 m²=100 cm×100 cm=10 000 cm², so multiply by 10 000.
Applying it
- AQA N13 and R1 include metric length, area, volume, capacity and compound measures.
- Use given conversion factors for unfamiliar imperial units; do not guess them.
Convert 72 km/h to m/s.
الصعوبة 2/5 · 140 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
72×1000/3600=20.
Match each conversion to its factor.
الصعوبة 2/5 · 140 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
Each dimension carries its own conversion; compound units convert numerator and denominator separately.
In your course
- AQA GCSE Mathematics (8300), Higher tier, specification section 3.1.
- Paper 1 is non-calculator: keep fractions, surds and π exact and show each step. On calculator papers, still write the expression before its value.
- Conversion factor: The multiplier that expresses the same quantity in another unit.
- Convert each dimension.
- Watch for: the area multiplier is the square of the length multiplier; the volume multiplier is its cube.