|Dimensional Analysis (The Factor Label Method)|
|Most calculations in science
involve measured quantities. In such calculations, the units in which
quantities are measured must be treated mathematically just as the numerical
parts of the quantities are. For example, in multiplying 1.2 cm by 2.0
cm, there are two separate calculations to be carried out.
First, it is necessary to multiply the two numbers: 1.2 X 2.0 = 2.4
Second, it is necessary to multiply the two units: cm X cm = cm2. The complete answer then, is 1.2 cm X 2.0 cm = 2.4 cm2.
This concept can be applied in the solution of many problems. The application depends on the use of a "conversion factor". A conversion factor is a fraction in which the numberator adn the denominator both represent the same measurement. For example, the fraction
100 cmis a unit factor since both the numerator and denominator represent the same length (one meter). The solved examples illustrate the use of unit factors in solving problems by dimensional analysis.
Table of Conversion Factors
||Convert 45.3 cm to its equivalent measurement
||Select a conversion factor which will convert
the unit "cm" to the unit "mm". The appropriate conversion factor is: 10
mm / 1 cm. Arrange the problem so that the given measurement, when multiplied
by the correct unit factor, will yield an answer with the proper label:
||Change a speed of 72.4 miles per hour to its equvalent
in meters per second.
|In this example, several conversion factors are
needed. One to change the miles into meters and the other to change hours
||The density of mercury is 13.6 g/mL. What
is the mass in kilograms of a 2 L commercial flask of mercury?
|Set up the problem so that the calculation will
yield a result with a mass in grams.
|Dimensional Analysis Practice
Problems Level 1
|Dimensional Analysis Practice Problems Level 2|
|Dimensional Analysis Practice Problems Level 3|