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When doing empirical formula problems, after you divide by the smallest number of moles, sometimes you get a decimal which you have to convert into a whole number for the formula. I know how what to multiply by when they're simple decimals like 0.5, 0.33, 0.66, 0.25, but how do I know what number to multiple by if the decimal is not one of those? Is there a faster way to do this that I am just missing?
I don't know if this method is faster per se, but I find it helpful to visualize the decimal in its fraction form when trying to determine what number to multiply by.
What generally works for me is trial and error. I sort of keep multiplying low value numbers until I find one that converts all the decimals into whole numbers, or at least close. It may not be the most efficient way but it definitely does give me the right answer.
I second the trial and error method. From what I've encountered, the decimals are usually the simpler ones you've listed that can be easily multiplied into whole numbers (or close to whole numbers). But trial and error has worked well for me in the past, and other than that, I'm not sure if there are any shortcuts.
They will usually be pretty obvious. The times that I've encountered a really weird number were due to personal error somewhere earlier in the problem. If the number is about +/- 0.1 off from a whole number, you can just round up or down. No multiplying necessary.
I usually do the trial and error method and for the most part it usually doesn't take too long until I find a number that satisfies making all the decimals into whole (or close to whole) numbers.
Like other commenters have said, trial and error is often an effective option. I also like to try to convert my decimals into fractions before I find which number to multiply them by. If you have a TI-30 this is pretty easy to do.
if you have a scientific calculator, there's a button that converts decimals to fractions and vice versa, it's denoted as F>D on mine. I usually use this to convert the decimal value to a fraction and then just multiply by that denominator.
There isn't really a faster way of doing it, but it helps to think about it as simple as possible. For instance, if I'm trying to find a number to multiply 1.33 by to get a whole number, I think about what number can I multiply 3 to get a number roughly close to 10. In this case, multiplying 3 by 3 equals 9, which is close enough to 10, allowing me to round up, so 1.33 multiplied by 3 is 3.99 which rounds up to 4. Similarly, 1.4 is too big of a number to round down, so multiplying by 2 equals 2.8, which is close enough to 3 for me to round up. Personally, this way makes finding the empirical formula much simpler.
With odd decimals, I usually go back to check my work just to make sure that it's all correct before I begin sorting out the odd decimal. Other posters have mentioned visualizing it as a fraction, and I think that that's a great way to go. For instance, if you get 0.636, that's 7/11. To quickly get rid of this fraction, multiply everything by 11 so that you are left with the coefficient of 7. This approach works best if the weird decimal is the only decimal you're left with.
I would use trial and error and try to estimate the lowest multiple of the numbers you have already and go from there.
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