Compare and convert metric units of weight

Learning Objectives Convert fluently between metric units of weight, including milligrams (mg), grams (g), and kilograms (kg). Interpret word problems to extract numerical values for geometric figures from given weights. Apply the Pythagorean theorem to find unknown side lengths of right triangles whose dimensions are derived from metric weight conversions. Use trigonometric ratios (SOH CAH TOA) to solve for unknown sides or angles in right triangles where dimensions are linked to weight values. Maintain unit consistency throughout multi-step problems that combine measurement conversion and geometry. Construct and solve proofs or problems involving 3D figures that contain right triangles with dimensions based on converted weights. How can the weight of a shipping container i...

TermDefinitionExample Metric Units of WeightA system of measuring weight based on the gram (g), using prefixes to denote multiples or fractions of the base unit. Key units are the kilogram (kg), gram (g), and milligram (mg).1 kilogram = 1000 grams. 1 gram = 1000 milligrams. Conversion FactorA numerical ratio used to convert a measurement from one unit to another without changing the value of the quantity.To convert 2.5 kg to grams, you use the conversion factor of 1000 g / 1 kg. So, 2.5 kg * (1000 g / 1 kg) = 2500 g. Pythagorean TheoremIn a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (legs).If the legs of a right triangle are 3 cm and 4 cm, the hypotenuse is 5...

Metric Weight Conversion Hierarchy To convert from a larger unit to a smaller unit, MULTIPLY by 1000 for each step (kg → g → mg). To convert from a smaller unit to a larger unit, DIVIDE by 1000 for each step (mg → g → kg). Use this rule as the first step in any problem to find the numerical values for your geometric calculations. For example, to go from kg to mg, you multiply by 1000 twice (1,000,000). Pythagorean Theorem a^2 + b^2 = c^2 Use this formula when you know two side lengths of a right triangle and need to find the third. 'a' and 'b' are the legs, and 'c' is the hypotenuse. Trigonometric Ratios \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \quad | \quad \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \quad | \...