What a conversion factor essentially represents is a relationship between two different units, i.e. a way to go from one unit to another.
Conversion factors are usually set up as ratios that allow for easier conversions between units. So, let's say you need to convert 25 g to kg. You would set up the conversion factor like this
#25# #"g" * (1 "kg")/(1000 "g") = 0.025# #"kg"#
This can be read as :
#25 "g times 1 kg for every 1000 g equals 0.025 kg"#.
#"1 kg"/("1000 g")# is your conversion factor. An important aspect is that all conversion factors must equal 1 if you replace one unit with another, like this:
#"1 kg"/("1000 g") = "1000 g"/("1000 g") = 1 #, and
#"1 kg"/("1000g") = "1 kg"/("1 kg") = 1#.
You could go from kg to g the same way
#"0.025 kg" * ("1000 g")/("1 kg") = "25 g"#
#0.025 "kg times 1000g for every 1 kg equals 25 g"#.
The most common examples of conversion factor utility in chemistry involve mass, moles, and molar mass. Here's an example:
You burn methane (#CH_4#) with enough oxygen, and receive 1 cent for every g of water you produce. How much money will you receive in dollars when you burn 50.0 g of methane?
#CH_4 + 2O_2 -> CO_2 + 2H_2O#
Let's solve this using a single chain of conversion factors
#"50.0 g " CH_4 * ("1 mole " CH_4)/(16.0 "g") * ("2 moles "H_2O)/("1 mole " CH_4) * ("18.0 g "H_2O)/("1 mole "H_2O) * ("1 cent ")/("1 g "H_2O) * ("1 dollar ")/("100 cents") = "1.125 dollars"#
#" 50 g of methane"# times #"1 mole of methane for every 16 g"# times #"2 moles of water for every 1 mole of methane"# times #"18 g of water for every 1 mole of water"# times #"1 cent for every 1 g of water"# times #"1 dollar for evey 100 cents"# #" equals 1.125 dollars"#.
Notice that we've converted from mass of methane to dollars using one long series of conversion factors.
Here's another example on this courtesy of another contributor:
http://socratic.org/questions/what-are-conversion-factors?source=search
