Unit Conversions (SQA National 5 Applications of Mathematics): Revision Note

Converting units

What are the conversion factors for units?

Lengths

• You need to know the metric conversions:

  • 1 cm = 10 mm

  • 1 m = 100 cm

  • 1 km = 1000 m

• You will be given any imperial conversions, such as:

  • 1 mile = 1.609 km

Masses

• You need to know the metric conversions:

  • 1 kg = 1000 g

Volumes

• You need to know the metric conversions:

  • 1 ml = 1 cm³

  • 1 L = 1000 ml

• You will be given any imperial conversions, such as:

  • 1 gallon = 4.546 L

Time

• You need to know the conversions:

  • 1 minute = 60 seconds

  • 1 hour = 60 minutes

What are the conversion factors for squared and cubic units?

Squared units

• You need to square the normal conversion factors

  • 1 cm² = 100 mm²

    • because 10² = 100

  • 1 m² = 10,000 cm²

    • because 100² = 10,000

Cubic units

• You need to cube the normal conversion factors

  • 1 cm³ = 1000 mm³

    • because 10³ = 1000

  • 1 m³ = 1,000,000 cm³

    • because 100³ = 1,000,000

How do I convert units using conversion factors?

• Multiply by the conversion factor to convert from the first unit to the second unit

  • e.g. 1 m = 100 cm

    • 3 m = (3 × 100) cm = 300 cm

• Divide by the conversion factor to convert from the second unit to the first unit

  • e.g. 1 L = 1000 ml

    • 7290 ml = (7290 ÷ 1000) L = 7.29 L

• You might have to use two conversion factors

  • e.g. 1 mile = 1.609 km

    • 0.4 miles = (0.4 × 1.609) km = 0.6436 km

  • and 1 km = 1000 m

    • 0.6436 km = (0.6436 × 1000) m = 643.6 m