1. Using Conversion Factors and Expressing Relationships Dimensional Analysis and Proportionality

2. Conversion Factor A ratio derived from the equality between two different units that can be used to convert from one unit to another. Ex. Expressed as a fraction where the product = 1

3. Dimensional Analysis A mathematical technique that allows you to use units to solve problems involving measurements. Ex. How many quarters are in 12 dollars? Ex. How many inches are in 2839.64 feet?

4. More examples Express a mass of 1876 g in kg. Express a distance of 12 km in cm. Convert 78 mi/hr into m/s.

5. Deriving Conversion Factors To use conversion factors, you must know the relationship between units (e.g. 12 inches = 1 foot) In Science, we will use the metric system. YOU MUST KNOW THE METRIC PREFIXES and their relationship to base units in order to use conversion factors. See Table 2, page 35. The equalities under “Example” show the conversion factors for each unit. Using these, you can always convert between the base unit and any other unit.

6. Proportionality Directly proportional = what happens to one quantity (x), happens to the other (y) If x doubles, y doubles y=xk Indirectly proportional = what happens to one quantity (x), the opposite happens to the other (y) If x doubles, y is halved y=k/x k is constant.

7. Examples A = l x w, describe proportionality of l and w, assume area remains constant. D = m/v, describe proportionality of m and D, if v remains constant.