Unit Conversions: Base & Non-Base Units

• Converting between exponential base units and non-base units involves understanding the relationship between different units and applying appropriate conversion factors or formulas.

Converting from Exponential Base Units to Non-Base Units

• Identify the exponential base unit and the target non-base unit.
• Determine the relationship or formula that connects the two units
• Apply the conversion factor or formula to convert the value from the base unit to the non-base unit
• Ensure that the units are consistent throughout the conversion process.
• Converting square meters (m²) to square feet (ft²) requires knowing the conversion factor between meters and feet (1 meter = 3.28084 feet) and then squaring that factor to convert square meters to square feet (1 m² = (3.28084 ft)² = 10.764 ft²).

Converting from Non-Base Units to Exponential Base Units

• Identify target exponential base unit
• Determine the relationship or formula that connects the two units.
• Apply the inverse of the conversion factor or formula to convert the value from the non-base unit to the base unit
• Ensure that the units are consistent throughout the conversion process.
• Converting square feet (ft²) to square meters (m²) requires knowing the conversion factor between feet and meters (1 foot = 0.3048 meters) and then squaring that factor to convert square feet to square meters (1 ft² = (0.3048 m)² = 0.0929 m²).

Area Conversion

• Area is a two-dimensional quantity, so when converting area units, the linear conversion factor must be squared.
• To convert square meters (m²) to square centimeters (cm²), since 1 m = 100 cm, then 1 m² = (100 cm)² = 10,000 cm².
• When converting from a non-base unit of area to a base unit of area, the same principle applies, but the inverse relationship is used.
• To convert square feet (ft²) to square inches (in²), since 1 ft = 12 in, then 1 ft² = (12 in)² = 144 in².

Volume Conversion

• Volume is a three-dimensional quantity, so when converting volume units, the linear conversion factor must be cubed.
• To convert cubic meters (m³) to cubic centimeters (cm³), since 1 m = 100 cm, then 1 m³ = (100 cm)³ = 1,000,000 cm³.
• When converting from a non-base unit of volume to a base unit of volume, the same principle applies, but the inverse relationship is used.
• To convert cubic feet (ft³) to cubic inches (in³), since 1 ft = 12 in, then 1 ft³ = (12 in)³ = 1,728 in³.

Steps for performing conversions

• Identify the given value and its unit.
• Identify the desired unit for the converted value.
• Find the appropriate conversion factor or formula that relates the given unit to the desired unit.
• Set up the conversion by multiplying the given value by the conversion factor in a way that cancels out the original unit and leaves the desired unit.
• Perform the calculation to obtain the converted value in the desired unit.
• Check the converted value to ensure it makes sense in the context of the problem.
• Include the appropriate units with the converted value to avoid ambiguity.

Examples for area and volume

• Conversion of Area:
  • Convert 10 square meters (m²) to square feet (ft²):
  • 1 m = 3.28084 ft
  • 1 m² = (3.28084 ft)² = 10.764 ft²
  • 10 m² = 10 × 10.764 ft² = 107.64 ft²
• Conversion of Volume:
  • Convert 5 cubic meters (m³) to cubic centimeters (cm³):
  • 1 m = 100 cm
  • 1 m³ = (100 cm)³ = 1,000,000 cm³
  • 5 m³ = 5 × 1,000,000 cm³ = 5,000,000 cm³

Common mistakes

• Forgetting to square or cube the conversion factor when dealing with area or volume, respectively.
• Using the wrong conversion factor or formula.
• Making errors in arithmetic during the conversion calculation.
• Not paying attention to units and ensuring they cancel out correctly during the conversion process.
• Rounding errors, especially when dealing with multiple steps in the conversion process.
• Not checking the reasonableness of the converted value in the context of the problem.