Factor-Label Method in Chemistry: Definition, Examples & Practice Problems

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  • 0:02 Factor-Label Method
  • 1:53 Simple Unit Conversions
  • 3:23 Derived Unit Conversions
  • 4:56 Lesson Summary
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Lesson Transcript
Instructor: Nathan Crawford

Nathan, a PhD chemist, has taught chemistry and physical science courses.

This lesson introduces the factor-label method for converting units. The basic technique is included as well as several examples of metric unit conversions and basic molar mass conversions found in chemistry.

The Factor-Label Method

Believe it or not, one simple method can be used to accomplish many of the basic calculations in chemistry. The method does not involve years of calculus courses or other higher level mathematics. In fact, the only skills that you need to perform this calculation method is the ability to multiply and divide. What is this calculation method? The name of this technique is known as factor-label!

Factor-label, also known as dimensional analysis in some circles, describes a technique to convert one quantity - a length, mass, or anything else for that matter - to another quantity. The technique relies on the use of equalities, called conversion factors, that provide the link between the unit being converted and the new unit of measure. The units, expressed as fractions, are multiplied together with the conversion factors arranged in such a way that all units cancel except the target unit.

To illustrate the factor-label process, consider the conversion of 250 gigabytes of computer memory to the actual number of bytes. The conversion factor in this case is expressed as 1 GB = 1 * 10^9 bytes (note that 1 * 10^9 is an example of scientific notation, a way of writing large numbers that expresses them as powers of 10, and is the same as 1,000,000,000. The factor-label conversion in this case places the 250 GB over 1. The conversion factor is arranged as a fraction, with the 1 GB as the denominator, and is multiplied by the 250 GB.

Conversion of GB to bytes using the factor-label method

Factor-Label Simple Unit Conversions

The factor-label method can be used to easily convert units from the Système International, or metric system. The metric system, a system of measurement that is used throughout the world, is based on powers of 10, as shown in the table below. The prefixes can be used to easily create conversion factors for the factor-label method. For example, 256 centimeters can be converted into kilometers by creating two conversion factors: 1 cm = 0.01 m and 1 km = 1,000 m.

SI Prefix Symbol Power of 10
giga- G 10^9
mega- M 10^6
kilo- k 10^3
deci- d 10^-1
centi- c 10^-2
milli- m 10^-3
nano- n 10^-9

Conversion of cm to km by the factor-label method

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