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Solving Sig Figs Involving Addition and Subtraction - Concept

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Teacher/Instructor Kendal Orenstein
Kendal Orenstein

Rutger's University
M.Ed., Columbia Teachers College

Kendal founded an academic coaching company in Washington D.C. and teaches in local area schools. In her spare time she loves to explore new places.

So you've taken a lot of calculations during your lab. Now you have to manipulate those calculations and add, or subtract them to get more information. So there are two pieces of information that you need to add. You have two pieces of data; one it's 11.352, and another piece of data is 10.4g. You need to add those two together. You want to make sure that your answer is significantly correct. Meaning it has the correct number of sig figs.

So when you put this in your calculator, you end up getting 21.752g. Then you turn it in to your teacher, and your teacher says nope you're wrong. You're like wait a minute, but my calculator said I was right. Your teacher is right. This is not the right answer. This is not.

So how do we find an answer that is significantly correct? We know about sig figs that the last digit is what we call an estimated digit. All measurements can only have one estimated digit. So when I put these again, I'm going to circle my estimated digit. In this case, it's always the last digit. We estimated that 2 there when we measured it, we also have 10.4. We estimated that 4 when we measured that too. So I'm circling it.

I'm going to add these by hand in order to understand why it works the way that it does. Anytime you work with an estimated digit, your answer is also estimated. So I'm going to bring bring down that 2. That is estimated, because it came from an estimated digit. I'm going to bring down that 5. 3 plus 4 is 7. It's estimated, I'm circling it. 1 plus 0 is 1. 1 plus 1 is 2, so obviously I got the same number numerically, but now I two circled numbers. This is grams. Our answer must only have 1 estimated digit. I'm writing that down. You might also hear that as a doubtful digit.

We have 2 here, so we want to have the estimated digit to the one that's closest to one other number. So these two don't matter. I'm dropping that. Our answer is 21.7g. That's our answer.

Now I don't want to have to do this everytime I do a Math problem. I don't want to have to circle number to see what happens. Did I make a mistake? I don't want to do that. So I'm going to write myself a rule. This is what the rule comes from. You might know this rule, but this is why the rule acts the way that it does. When adding or subtracting, not multiplying and dividing this works for addition, and subtraction data your answer is as precise as the least precise measurement.

What the heck is precision or how does that work? Well, precision and deciding which number is more precise, has to do with decimal points. So this ends in a thousandths, very precise. This ends in the tenths, precise, but not as precise. This is more precise. This is our least precise. So our answer ended up in the tenths, my answer too must end in the tenths as well.

So basically you're talking about decimal places. So hopefully this method helps you understand why this rule is in existence. You're only allowed to have one estimated digit. This only works for addition and subtracting; significant digits. You're going to come across this not only in Chemistry, but the rest of your academic scientific life.

So you have to make sure you understand why sig figs work the way that they do, and understanding how to use the rules properly to get the correct and most significant answer you can. Hope that helped.