Measurements and Dimensional Analysis

Why do we have standard measurements? A measurement consist of two parts Number Scale Two Major systems English system Used in the United States Pounds Feet gallons Metric system SI System – based on the metric system and units derived from it

SI Unit of Measurement Quantity SI Unit Symbol Length Meter m Volume Cubic meter Liter m3 L Mass Kilogram Kg Density Grams per cubic centimeter g/cm3 Temperature Kelvin K Time Second s

SI Prefixes Conversion Factor: a ratio of equivalent measurements 109 106 1000 100 10 0.1 0.01 0.001 10-6 10-9 Conversion Factor: a ratio of equivalent measurements 1 m = 10 dm 1 m = 100 cm 1 m = 1000 mm 1 liter = (1 dm)3 = (10cm)3 = 1000cm3 4

Conversion Factors Derived Units Combination of SI units from Derived units Conversion Factors: ratio derived from the equality of two different units that can be used to convert from one to the other Use units to help derive and cancel (algebraic) 5

Solving Problems using Dimensional Analysis Analyze Identify given Identify needed Plan Use units to cancel Compute Plug in #s Evaluate Examine to determine if reasonable

Sample Problems 1. 0.057 m to km 2. 13 cm3 to mL 3. 0.986 hours to seconds 4. 3.004 L to mL 5. 86 kg to g 6. 24 cm3 to L 7. 56,000 μg to kg 8. 56 km to mm ***Always show your work***