Compare and convert customary units (Summary)

Learning Objectives Recall and apply conversion factors for customary units of length, area, and volume. Convert measurements between different customary units (e.g., inches to feet, square feet to square yards) within a single problem. Ensure unit consistency before applying the Pythagorean theorem or trigonometric ratios. Solve multi-step geometry problems involving right triangles where initial measurements are given in mixed customary units. Calculate the area and perimeter of right triangles, expressing the final answer in a specified customary unit. Determine the volume of 3D figures derived from right triangles (e.g., prisms, pyramids) and convert the result between cubic customary units. Ever tried to build a ramp where the height is in inches and the base is in feet...

TermDefinitionExample Customary SystemThe system of measurement used primarily in the United States, including units like inches, feet, yards, miles, pounds, and gallons.Length is measured in inches (in), feet (ft), yards (yd), and miles (mi). Conversion FactorA ratio or fraction which represents the relationship between two different units and is equal to one. It is used to convert a measurement from one unit to another.To convert feet to inches, the conversion factor is `(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 is used to convert units by setting up conversion factors so that unwanted units cancel out.`36 \text{ in} \times \frac{1 \text{ ft}}{12 \text{ in}} = 3 \...

Key Length Conversion Factors 1 ft = 12 in 1 yd = 3 ft 1 mi = 5280 ft These are the fundamental relationships for converting customary units of length. Use them to build conversion factors for dimensional analysis. Pythagorean Theorem Unit Mandate a^2 + b^2 = c^2, where units(a) = units(b) = units(c) Before applying the Pythagorean theorem to find a missing side of a right triangle, you MUST convert all given side lengths to a single, consistent unit. Area Conversion Formula Area_{new} = Area_{old} \times (\frac{\text{linear unit}_{new}}{\text{linear unit}_{old}})^2 To convert an area from one unit to another (e.g., square feet to square inches), multiply the original area by the square of the linear conversion factor.