Unit Conversions | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Converting Units

How do I convert between units for lengths?

• Conversion of metric units involves multiplying or dividing by powers of 10.
• Basic conversions to remember:
  • 1 cm = 10 mm
  • 1 m = 100 cm
  • 1 km = 1000 m
• To decide whether to multiply or divide, consider if the number of units increases or decreases.
  • Example: Since the number of mm is 10 times greater than cm, mm = cm × 10.
• You can perform conversions in stages. For example, convert kilometers to meters, then meters to centimeters.
• When given an imperial conversion (e.g., miles to kilometers), ratios can be used for conversions.
  • Example: There are 5 miles in 8 kilometers. To find how many miles are in 13 kilometers, solve using ratios.
    5 : 8 = x : 13

How do I convert units for mass?

• Conversion of metric units involves multiplying or dividing by powers of 10.
• Understanding basic conversions is key:
  • 1 gram (g) = 1000 milligrams (mg)
  • 1 kilogram (kg) = 1000 grams (g)
  • 1 tonne = 1000 kilograms (kg)
• Imperial conversions, like pounds to kilograms, can be solved using ratios.
  • For example, with 2.2 pounds in 1 kilogram, to convert 10 pounds to kilograms, you'd calculate accordingly.
    2.2 : 1 = 10 : x

How do I convert units for volume/capacity?

• For metric units, conversion entails multiplying or dividing by powers of 10.
• Essential conversions to remember:
  • 1 liter (l) = 1000 milliliters (ml)
  • 1 centiliter (cl) = 10 milliliters (ml)
  • 1 milliliter (ml) = 1 cubic centimeter (cm³)
• Imperial conversions, such as pints to liters, can be tackled with ratios.
  • For instance, 1.75 pints in 1 liter means to find how many liters are in 5 pints, you'd apply the appropriate ratio.
    1.75 : 1 = 5 : x

Squared & Cubic Units

How do I convert between squared units?

• Converting between squared units, commonly used for areas, requires special attention. 
• Remember to square the conversion rates because area is two-dimensional. 
  • The presence of "squared" in the units can serve as a helpful reminder of this concept.
• Basic conversion examples include:
  • 1 cm² = 10² mm² = 100 mm²
  • 1 m² = 100² cm² = 10,000 cm²
  • 1 km² = 1,000² m² = 1,000,000 m²
• For less common conversions, remember:
  • 1 hectare (ha) = 10,000 m²
• When dealing with imperial conversions for lengths, such as miles to kilometers:
  • Express the conversion as a ratio (e.g., Miles to kilometers is 5:8)
  • Square the numbers to obtain the ratio for area unit conversion (e.g., Miles² to kilometers² is 25:64)

How do I convert between cubed units?

• Cubing Conversion Rates:
  • When converting units for volume, it's essential to cube the normal conversion rates. This is because volume is three-dimensional, and the units being cubed help in remembering this concept.
• Basic Conversions:
  • 1 cm³ = 10³ mm³ = 1000 mm³
  • 1 m³ = 100³ cm³ = 1,000,000 cm³
  • 1 km³ = 1000³ m³ = 1,000,000,000 m³
• Imperial Conversions for Lengths:
  • When dealing with imperial conversions like miles to kilometers for lengths, write the conversion as a ratio (e.g., 5 : 8).
  • To convert the units for volume, cube the numbers in the ratio. For example, converting miles³ to kilometers³ would be 125 : 512.