Dimensional Analysis

The Factor-Label Method

• In this method, a quantity described in one unit is converted into an equivalent quantity described in one unit is converted into an equivalent quantity described in a different unit by using a conversion factor that expresses the relationship between units.

• Starting Quantity x Conversion Factor = Equivalent Quantity

The Factor-Label MethodAn example:1 km = 0.6214 miConversion factors between kilometers and miles:1km/0.6214 mi or 0.6214 mi/1 km = 1• Multiplying by a conversion factor is equivalent to multiplying to multiplying by 1

and so does not change the size of the quantity being multiplied. 1km or 0.6214 mi 0.6214 mi 1 km the same quantities The key to the factor-label method of problem solving is that units are treated like numbers and can be multiplied and divided.The idea when solving a problem is to set up an equation so that all unwanted units cancel, leaving only the desired units. Usually, it’s best to start by writing what you know and then manipulating that known quantity.

The Factor-Label Method

• Example:Convert 26.22 mi into km.26.22 mi x 1km = 42.20 km 0.6214 mi starting conversion equivalentquantity factor quantity

The Factor-Label Method

• It gives the right answer only if the equation is set up so that the unwanted units cancel. If the equation is set up in any other way, the units won’t cancel and you won’t get the right answer.

• The examples:• A) Convert deciliters to milliliters• 1 L = 10dL = 1000 mL 1 dL = 100 mL• The conversion factors: 1 dL or 100 mL 100 mL 1 dL

The Factor-Label Factor

• An example: Convert 0.75 lb to grams.• 1lb = 454 g• The conversion factors: 1 lb or 454 g 454 g 1 lb• 0.75 lb x 454 g = 340 g 1 lb