Convert rates and measurements: customary units

Learning Objectives Correctly identify and apply conversion factors for customary units of length, volume, and weight. Convert measurements involving multiple steps within the customary system (e.g., miles to inches). Use dimensional analysis to convert rates with compound units (e.g., feet per second to miles per hour). Convert squared and cubed units accurately (e.g., square feet to square yards, cubic inches to cubic feet). Solve real-world problems by applying measurement and rate conversions, including those related to geometric figures. Analyze units within a problem to determine the necessary conversion steps and validate the final answer. Your favorite athlete runs the 40-yard dash in 4.5 seconds. 🏃💨 How fast is that in miles per hour, and could they outrun a city...

TermDefinitionExample Customary SystemThe system of measurement primarily used in the United States. It includes units like inches, feet, miles, ounces, pounds, cups, pints, quarts, and gallons.A road sign indicating a speed limit of 65 miles per hour uses customary units. Conversion FactorA ratio or fraction which represents the relationship between two different units of measurement and is equal to one. It is used to convert a measurement from one unit to another.The relationship 1 foot = 12 inches can be written as the conversion factor (1 ft / 12 in) or (12 in / 1 ft). Dimensional AnalysisA problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. It involves strategically multiplying by conversion factors to cancel ou...

Dimensional Analysis Formula Desired Quantity = Given Quantity \times \frac{\text{Unit A}}{\text{Unit B}} \times \frac{\text{Unit C}}{\text{Unit A}} \times \dots Start with the given quantity. Multiply by a series of conversion factors arranged so that the unwanted units in the numerator cancel with the units in the denominator of the next factor, until only the desired units remain. Area and Volume Conversion Rule If 1\text{ ft} = 12\text{ in}, then 1\text{ ft}^2 = (12\text{ in})^2 = 144\text{ in}^2, and 1\text{ ft}^3 = (12\text{ in})^3 = 1728\text{ in}^3. When converting units of area or volume, you must square or cube the entire conversion factor, including both the number and the unit. A common mistake is to only convert the unit without squaring or cubing the numerical...