One of the best ways to avoid small mistakes is to include units when you plug your numbers in and to carry those units all the way through without skipping any steps.
Take a look at the problem below for an example. Here, we're given the kinetic energy and mass of an object and need to solve for its velocity:
Take a look at the problem below for an example. Here, we're given the kinetic energy and mass of an object and need to solve for its velocity:
I wrote all of the units into the solution, didn't skip any steps, and plugged my answer (including the units) back into the original equation to make sure the answer was right. I converted joules into simpler units (kg * m2 / s2) in order to make the units canceled and caught a potential mistake where I might have forgotten to convert grams to kilograms.
If you do this consistently, most of your small mistakes should go away on their own. Showing your work takes discipline, but it's a lot better than having to solve problems over and over again on homework, or, worse, get them wrong on tests without realizing it.
Chemistry problems in upper-division college classes involve calculus and statistics and are much harder than the one I just solved. Ironically, as a problem gets harder, it's more important to show every step of the solution, as a single mistake causes you to have to do the entire problem over again.
If you want me to write up a solution for a problem you're working on right now, please contact me. I'd be happy to do one for you for free!
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