Cambridge Metric Units Notes

Metric Units

  • The metric system employs various units for length, mass, and capacity.

Length

  • Common metric units:

    • Kilometre (km)

    • Metre (m)

    • Centimetre (cm)

    • Millimetre (mm)

Mass

  • Common metric units:

    • Tonne (t)

    • Kilogram (kg)

    • Gram (g)

    • Milligram (mg)

Capacity

  • Common metric units:

    • Litre (L) or (l)

    • Millilitre (ml)

Prefixes Explained

  • Centi-: from Latin "centum" meaning hundred (1 cm = 1/100 m)

  • Milli-: from Latin "mille" meaning thousand (1 mm = 1/1000 m)

  • Kilo-: from Greek "khilloi" meaning thousand (1 km = 1000 m)

Practical Experiences

  • Estimation of lengths, volumes, and capacities is vital before completing exercises.

Conversions

Length Conversions

  • 1 km = 1000 m

  • 1 m = 100 cm

  • 1 m = 1000 mm

Worked Examples:

  1. Convert 5.8 km to meters:

    • 5.8 km × 1000 m/km = 5800 m

  2. Convert 2.3 km to cm:

    • 2.3 km = 2.3 × 1000 m = 2300 m; then 2300 m × 100 cm/m = 230000 cm

  3. Convert 4700 mm to m:

    • 4700 mm ÷ 1000 mm/m = 4.7 m

Mass Conversions

  • 1 tonne = 1000 kg

  • 1 kg = 1000 g

  • 1 g = 1000 mg

Worked Examples:

  1. Convert 8300 kg to tonnes:

    • 8300 kg ÷ 1000 kg/tonne = 8.3 tonnes

  2. Convert 2.5 g to mg:

    • 2.5 g × 1000 mg/g = 2500 mg

Capacity Conversions

  • 1 L = 1000 ml

  • 1 m³ = 1000 L

  • 1 cm³ = 1 ml

Worked Examples:

  1. Calculate 3 L + 1500 ml:

    • 3 L = 3000 ml, Total = 3000 + 1500 = 4500 ml

  2. 0.75 L + 6300 ml:

    • 0.75 L = 750 ml, Total = 750 + 6300 = 7050 ml

Area and Volume Conversions

  • Converting areas and volumes is more complex than lengths

  • For example:

    • Area: 1 m² = 10,000 cm² (1 m = 100 cm)

    • Volume: 1 m³ = 1,000,000 cm³ (1 m = 100 cm)

Exercises and Examples:

  • Convert various units between lengths, masses, capacities, areas, and volumes as practiced in exercises.

Circle Geometry

  • Circumference and Area of a circle:

    • Circumference = 2πr

    • Area = πr²

Worked Example:

  1. Calculate the circumference of a circle with a radius of 3 cm:

    • Circumference = 2π(3) = 6π cm

  2. The area of a circle with a radius of 5 cm:

    • Area = π(5)² = 25π cm².