Problem solving involves developing a plan, and mapping out a pathway through a problem before solving. Any two measurements that are equal to one another but expressed in different units can be written as a ratio. A ratio of equivalent measurements is called a conversion factor and is equal to unity. Conversion factors are used in the problem solving technique of dimensional analysis. A ratio of equivalent measurements has two forms. The correct conversion factor for solving a particular problem will have the known unit in the denominator and the unknown unit in the numerator. Conversion problems in which you are asked to express a measurement in some other unit are easily solved using dimensional analysis. In dimensional analysis, units are used to help write the solution to a problem. More than one conversion factor may be required in some more complex conversion problems. The given measurement in a rate problem has a ratio of units. Rate problems may be solved by converting the unit in the numerator followed by converting the unit in the denominator.

Chapter VocabularyConversion factor:

how measurements are related to each other.

Dimensional anaylsis: using units to figure out

problemsunit

Grams, ounces, and other labels which tell you what type of quantity you are using.

density How mass is related to volume.

Boling point The temperature at which the vapor

pressure equals atmospheric pressuretemperature

A measure of the hotness or coldness of a substance

Dimensional AnalysisStep 1: copy the knownStep 2: identify and copy the conversion

factorStep 3: multiply the numerator, divide the

denominator

More vocabularyCelsius

Metric measurement of temperaturevolume

Length x width x height or area x height. How much space is occupied by an object.

mass The quantity of matter

known The thing given in the problem.

UnknownThe thing you are trying to find in the problem

5280 feet = 1 mile 16 oz = 1 pounds 12 inches = 1 foot 1 pint = 473 milliliters 1 ton = 2000 pounds 5 carats = 1 kilograms

32 miles = ? feet

32 miles_5280 feet_

1 mile = 168960 feet = 170,000 feet

45 oz = ? pounds

45 oz _1 pound_16 oz

= 2.8125 pound = 2.8 pound

Step 1: copy the knownStep 2: identify and copy the conversion factorStep 3: multiply the numerator, divide the denominator

3.4 pints = ? milliliters

5.6 pounds = ? tons

5280 feet = 1 mile 16 oz = 1 pounds 12 inches = 1 foot 1 pint = 473 milliliters 1 ton = 2000 pounds 5 carats = 1 kilograms

3.4 pints _473 mL_1 pint

= 1608.2 mL = 1600 mL

5.6 pounds_1 ton_2000

pounds = 0.0028 tons