1) Dimensional Analysis

• Dimensional analysis helps ensure that solutions to problems have the correct units.
• A conversion factor is a fraction whose numerator and denominator have equal quantities expressed in different units.
• Example: 1ft = 12in, can be written as 1ft/12in or 12in/1ft.
• A conversion factor is used to convert a quantity from one unit to another.
• Example: 6in x (1ft/12in) = ½ ft, 2ft x (12in/1ft) = 24in.
• Example model: given unit x (desired unit/given unit) = desired unit
• Sometimes two or more conversion factors are needed.
• Example: 2yd x (3ft/1yd) x (12in/1ft) = 72in.
• Some conversions involve altering the measure.
• For example, instead of converting from length to length, some conversions involve converting form volume to mass.
• Example: convert 3.00in³ of gold to grams, density of gold is 19.3g/1cm³.
• Continued: First you must convert the conversion factor, 2.54cm/1in, into volume: (2.54cm)³/(1in)³ = 16.39cm³/1in³.
• Continued: 3.00in³ x (16.39cm³/1in³) x (19.3g/1cm³) = 948g.