Measurement
Why Measurement Matters
Measurement lets us describe and compare the physical world using numbers. Two major systems exist: the metric system (used by most of the world) and the imperial system (still used in the UK and US for some everyday measurements). Understanding both โ and converting between them โ is an essential skill.
Key Terms
- Metric system โ a decimal-based measurement system using units divisible by 10
- Imperial system โ an older system using units such as inches, pounds, and pints
- Conversion factor โ the number you multiply or divide by to change from one unit to another
- Capacity โ the amount of liquid a container can hold
Metric Units: Length
The metric system uses multiples of 10, which makes conversions straightforward โ simply multiply or divide by powers of 10.
| Unit | Equivalent |
|---|---|
| 1 km (kilometre) | 1,000 m |
| 1 m (metre) | 100 cm |
| 1 cm (centimetre) | 10 mm |
| 1 m | 1,000 mm |
Memory tip: kilo = 1,000; centi = 1/100; milli = 1/1,000
Metric Units: Mass
| Unit | Equivalent |
|---|---|
| 1 tonne | 1,000 kg |
| 1 kg (kilogram) | 1,000 g |
| 1 g (gram) | 1,000 mg |
Metric Units: Capacity
| Unit | Equivalent |
|---|---|
| 1 litre | 1,000 ml |
| 1 cl (centilitre) | 10 ml |
Converting Between Metric Units
The rule is simple:
- Larger to smaller unit โ multiply (you need more of the smaller unit)
- Smaller to larger unit โ divide (you need fewer of the bigger unit)
Worked Examples:
- 3.5 km to metres: 3.5 ร 1,000 = 3,500 m
- 2,500 ml to litres: 2,500 รท 1,000 = 2.5 litres
- 4.2 kg to grams: 4.2 ร 1,000 = 4,200 g
- 850 cm to metres: 850 รท 100 = 8.5 m
Comparing Units
Before comparing measurements, always convert everything to the same unit:
Are 1.5 m, 150 cm, 1500 mm, and 0.0015 km the same?
- 1.5 m = 150 cm = 1,500 mm = 0.0015 km โ yes, all equal!
Worked Example: Order 0.45 km, 430 m, 4,600 cm from smallest to largest.
- 0.45 km = 450 m
- 430 m = 430 m
- 4,600 cm = 46 m
- Order: 46 m, 430 m, 450 m โ 4,600 cm < 430 m < 0.45 km
Imperial Units
| Imperial unit | Imperial equivalent | Metric equivalent |
|---|---|---|
| 1 foot | 12 inches | โ 30.5 cm |
| 1 inch | โ | โ 2.54 cm |
| 1 mile | 1,760 yards | โ 1.6 km |
| 1 pound (lb) | 16 ounces | โ 454 g |
| 1 stone | 14 pounds | โ 6.35 kg |
| 1 pint | โ | โ 568 ml |
| 1 gallon | 8 pints | โ 4.5 litres |
These conversions are approximate โ memorise the most commonly used ones.
Imperial to Metric Conversions
Worked Examples:
- 5 miles to km: 5 ร 1.6 = 8 km
- 3 inches to cm: 3 ร 2.54 = 7.62 cm
- 10 pounds to grams: 10 ร 454 = 4,540 g (or about 4.54 kg)
Common Mistakes
- Mistake: multiplying instead of dividing (or vice versa) when converting. Fix: ask "am I going to a bigger or smaller unit?" Bigger unit = divide; smaller unit = multiply.
- Mistake: mixing up mass and weight. Fix: mass is measured in kg/g; weight in physics is a force measured in newtons.
- Mistake: confusing ml and cl. Fix: 1 cl = 10 ml; 100 cl = 1 litre.
- Mistake: writing 0.0015 km as larger than 1.5 m because 0.0015 looks small. Fix: convert to the same unit before comparing.
Tips and Tricks
- Remember the prefix ladder: kilo (ร1,000) โ base unit โ centi (รท100) โ milli (รท1,000)
- For km to miles, a quick estimate: divide km by 8 and multiply by 5. So 80 km โ 50 miles.
- A standard 500 ml water bottle holds half a litre โ a useful reference point.
- Bathroom scales often show stones and pounds in the UK โ knowing 1 stone = 14 pounds helps decode them.