Compare and convert metric units

Learning Objectives Convert between common metric units of length (mm, cm, m, km) within a geometric context. Correctly convert metric units of area (mm², cm², m²) by squaring the corresponding length conversion factor. Apply metric conversions to find unknown side lengths in right triangles using the Pythagorean theorem. Solve for unknown angles and sides in right triangles using trigonometric ratios (SOH CAH TOA) when given mixed units. Calculate the perimeter and area of right triangles, ensuring all measurements are in a consistent unit before calculation. Analyze and solve multi-step word problems involving right triangles that require metric unit conversions. An architect's blueprint shows a support beam's height as 300 cm and its shadow as 4 m. How can you f...

TermDefinitionExample Metric System (SI)A decimal-based system of measurement where units are related by powers of 10. The base unit for length is the meter (m).Length units include kilometer (km), meter (m), centimeter (cm), and millimeter (mm). Conversion FactorA ratio equal to one that expresses the same quantity in two different units. It is used to convert from one unit to another.The conversion factor between meters and centimeters is (1 m / 100 cm) or (100 cm / 1 m). 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 ensure units cancel out correctly during conversions.To convert 2.5 km to m: 2.5 km * (1000 m / 1 km) = 2500 m. The 'km' units cancel out. Unit Consi...

Metric Length Conversion To convert from a larger unit to a smaller unit, multiply by a power of 10. To convert from a smaller unit to a larger unit, divide by a power of 10. Use this to establish unit consistency. For example, to convert 1.2 meters to centimeters, you multiply by 100 (1.2 * 100 = 120 cm). To convert 540 mm to meters, you divide by 1000 (540 / 1000 = 0.54 m). Metric Area Conversion Area_new = Area_old * (Linear Conversion Factor)² When converting area, you must square the linear conversion factor. For example, since 1 m = 100 cm, the area conversion factor is (100)², so 1 m² = 10,000 cm². Pythagorean Theorem a^2 + b^2 = c^2 In a right triangle with legs 'a' and 'b' and hypotenuse 'c', this formula relates the side length...