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 — and converting between them — is an essential skill.

Key Terms

• Metric system — a decimal-based measurement system using units divisible by 10
• Imperial system — an older system using units such as inches, pounds, and pints
• Conversion factor — the number you multiply or divide by to change from one unit to another
• Capacity — the amount of liquid a container can hold

Metric Units: Length

The metric system uses multiples of 10, which makes conversions straightforward — simply multiply or divide by powers of 10.

Memory tip: kilo = 1,000; centi = 1/100; milli = 1/1,000

Metric Units: Mass

Metric Units: Capacity

Converting Between Metric Units

The rule is simple:

• Larger to smaller unit → multiply (you need more of the smaller unit)
• Smaller to larger unit → divide (you need fewer of the bigger unit)

Worked Examples:

• 3.5 km to metres: 3.5 × 1,000 = 3,500 m
• 2,500 ml to litres: 2,500 ÷ 1,000 = 2.5 litres
• 4.2 kg to grams: 4.2 × 1,000 = 4,200 g
• 850 cm to metres: 850 ÷ 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 — 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 → 4,600 cm < 430 m < 0.45 km

Imperial Units

These conversions are approximate — memorise the most commonly used ones.

Imperial to Metric Conversions

Worked Examples:

• 5 miles to km: 5 × 1.6 = 8 km
• 3 inches to cm: 3 × 2.54 = 7.62 cm
• 10 pounds to grams: 10 × 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 (×1,000) → base unit → centi (÷100) → milli (÷1,000)
• For km to miles, a quick estimate: divide km by 8 and multiply by 5. So 80 km ≈ 50 miles.
• A standard 500 ml water bottle holds half a litre — a useful reference point.
• Bathroom scales often show stones and pounds in the UK — knowing 1 stone = 14 pounds helps decode them.