Unit Conversion - Changing Between Systems
Unit conversion is the skill of expressing the same measurement in a different unit. It is used constantly in science, cooking, engineering, travel, and everyday life. The key principle: multiply by the conversion factor when going to a smaller unit, divide when going to a larger one.
How Conversion Factors Work
A conversion factor is a fraction equal to 1, where the numerator and denominator express the same quantity in different units. Multiplying by it changes the unit without changing the value.
Example: 1 km = 1,000 m, so (1,000 m / 1 km) = 1. 5 km × (1,000 m / 1 km) = 5,000 m.
Metric to Metric Conversions
| Conversion | Factor | Example |
|---|---|---|
| km to m | × 1,000 | 3 km = 3,000 m |
| m to cm | × 100 | 2.5 m = 250 cm |
| cm to mm | × 10 | 4.7 cm = 47 mm |
| kg to g | × 1,000 | 0.85 kg = 850 g |
| l to ml | × 1,000 | 1.25 l = 1,250 ml |
Metric to Imperial Conversions
| Metric | Imperial | Approx. factor |
|---|---|---|
| 1 cm | 0.394 inches | cm ÷ 2.54 = inches |
| 1 km | 0.621 miles | km × 0.621 = miles |
| 1 kg | 2.205 pounds | kg × 2.205 = lb |
| 1 litre | 1.76 pints (UK) | l × 1.76 = pints |
| 1 litre | 0.264 gallons (US) |
Temperature Conversion
| From | To | Formula |
|---|---|---|
| Celsius | Fahrenheit | F = (C × 9/5) + 32 |
| Fahrenheit | Celsius | C = (F − 32) × 5/9 |
| Celsius | Kelvin | K = C + 273.15 |
Worked Examples
7.5 × 0.621 = 4.658 miles.
65 × 2.205 = 143.3 lb.
F = (20 × 9/5) + 32 = 36 + 32 = 68 °F.
2 × 240 = 480 ml. 480 ÷ 1,000 = 0.48 l.
Key Takeaways
- A conversion factor is a fraction equal to 1 that changes the unit of a quantity.
- In metric: conversions are always powers of 10 – multiply or divide.
- Keep track of units at every step to avoid errors (dimensional analysis).
- Approximate conversions are fine for everyday use; exact ones are needed in science.
Practice Questions
- Convert 4.5 miles to kilometres. (1 mile ≈ 1.609 km.)
- Convert 12 pounds to kilograms. (1 lb ≈ 0.454 kg.)
- A container holds 5 gallons. Convert to litres. (1 UK gallon ≈ 4.546 l.)
- Convert 35 °C to Fahrenheit.
- A car fuel tank holds 50 litres. How many UK gallons is that?
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