Metric and compound-unit conversions · Higher
| English | 中文 | Pinyin |
|---|---|---|
| conversion factor/kənˈvɜːʃn ˈfæktə/ | 换算因子 | huàn suàn yīn zi |
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.
Choose the mathematical structure
- 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.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines conversion factor?
The multiplier that expresses the same quantity in another unit.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
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.
Multiply 0.16 by 100²: 1600.
Test a tempting shortcut
- 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.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
To convert square metres to square centimetres, multiply by 100. This claim is false. Explain which definition or assumption it violates.
Convert 0.002 m³ to litres.
0.002×1,000,000=2000 cm³; divide by 1000 for 2 litres.
To convert square metres to square centimetres, multiply by 100.
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.
Interpret a new situation
- 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.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Convert 72 km/h to m/s.
72×1000/3600=20.
Match each part of a complete solution to its purpose.
An assumption justifies the model; a check tests the result; interpretation connects it to the question.
Use this in your course
- 8300 · Higher · 3.1. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
The multiplier that expresses the same quantity in another unit. Choose the relationship, show the method, check its assumptions and interpret the result.