 So here's our problem. Say we've done a mass percent analysis of a sample and we find that it's composed of 81.7% carbon and 18.3% hydrogen. The sequence of calculations that you go through is nicely summarized by this little rhyme which I picked up from Bergman and Sam's in their chemistry videos. Percent to mass, master mole, divide by small, times till whole. Let's go through it step by step. I'm going to write this out so that at each step I'm showing the ratio. So I'll start with the ratio of percentages of carbon to hydrogen. The first step is then to convert the percentage into a mass in grams. This is dead easy. You just assume that you have a total mass of 100 grams and then the masses of the individual elements will be the same as their percentages. So now we have the mass ratio between the two elements. Okay, so the second step, we need to convert these masses into moles. This is a simple mass mole conversion which we'll do over here. 81.7 grams of carbon divided by the molar mass of carbon which is 12.01 grams per mole gives me 6.80 moles of carbon. And 18.3 grams of hydrogen divided by 1.008 grams per mole that gives me 18.2 moles of hydrogen. So that gives us the mole ratio of carbon to hydrogen. But we still need to get it down to the simplest mole ratio. And that leads us to step number three. How do you simplify a ratio? Well you divide by the lowest common factor. So here we're going to divide through by the smallest of the two numbers. That will give us a ratio of 1 to something. So we divide through by 6.80 and that simplifies the ratio to 1 to 2.67. Now we know it's impossible to have less than a whole atom. So this ratio, because it's eventually going to represent numbers of atoms in a molecule, has to be made into a whole number ratio. So the last step, times till whole, just involves multiplying through by a factor until we have a whole number ratio. Now if you're good with fractions and decimals you'll see already what we have to multiply through by. But let me give you a cheat sheet. If your number ends in 0.5 then it means it's something and a half. And if you multiply through by 2 it will become a whole number. If it ends in 0.33 or 0.67 or close to then it's something and a third or something and two thirds. And you'll need to multiply through by 3 to make that fraction a whole number. And if it ends in 0.25 then it's something and a quarter and you multiply through by 4. In this case we need to multiply through by 3. And when you do that you find that the ratio is 3 to 8. So the empirical formula of our compound is C3H8. Let's try another. A compound containing only hydrogen, sulfur and oxygen is found to be composed of 2.46% hydrogen and 58.48% oxygen. Determine its empirical formula. First write out the percentages as a ratio. Note that we haven't been given the percentage of sulfur but we can work it out because the percentages must add up to 100%. Now convert them to masses, just a matter of changing the units. Now convert each mass into moles by dividing by the molar mass for that element. And that gives us a ratio of 2.44 to 1.22 to 3.66. Now we divide through by the smallest of those numbers which is 1.22 and that gives us 2 to 1 to 3. So in this case we didn't need to do the final step because the third step already gave us a whole number ratio. And our empirical formula is H2SO3.